Explain how to find the equation of a line given the point (5,3) and it has a y-intercept of 13.

Question

I have been and still am                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       perplexed on this question for hours, would appreciate the help. :(

Joel Runevic · Accepted Answer

Hey @Patrica Nwoke,

Glad to see you on the site :).

The general equation of a straight line is y = mx + c.

The c refers to the y-intercept, so the value of the y-coordinate when the straight line crosses the y-axis. You have this value as it is 13.

You also have a pair of coordinates (5,3) where x is 5 when y is 3 and vice versa - coordinates are always given in the form (x,y).

So what we can write so far is:

3 = 5m + 13

All we need to do now is solve for m. We can do this by rearranging the equation.

First, we minus 13 from both sides to get rid off the +13 on the righthand-side of the equation:

3 - 13 = 5m + 13 - 13

Which becomes:

-10 = 5m.

Now, we divide both sides by 5 to get -2 = m.

Et voila, we have figured out the value of m to be -2.

Going back to our general equation: y = mx + c. We now know the value of both m and c, so we can write the general equation as:

y = -2x + 13

That is the answer! Using this, you can figure out what the value of y will be for any given x value.

Let me know if you have any more questions! :)

Joel Runevic · Answer

No worries Patrica, any time! :)

Patrica Nwoke · Answer

Thank you so much Joel! You're a lifesaver! :D