Firstly, we need to find the gradient of the line segment AB. We can do this by calculating the change in y divided by the change in x. The change in y between points A and B is 20 and the change in x is 4. Dividing these two numbers and we get the gradient of AB to be 5.
We need an equation of a line that is perpendicular to AB, so we do the negative reciprocal of the gradient (this is a rule that you must remember!). In other words, the gradient is ( -1/5). Does this bit make sense?
Now, we know that the gradient of the line is -1/5 or -0.2. We don't, however, know the y-intercept of the line. So we know that the line has the form:
y = -0.2x + c. But, we know that the line passes through point C. So, we can just substitute the co-ordinates of c into our above equation.
We therefore get:
-7 = (-0.2 * -5) + c
-7 = 1 + c
-8 = c
So we now know that the equation of the straight line is y = -0.2x - 8.
But can you see that the question asks for where a and b are integers?
Therefore we have to bring the -0.2x to the other side and multiply both sides by 5 so that we get rid of any fractions.
Hey, of course!
Firstly, we need to find the gradient of the line segment AB. We can do this by calculating the change in y divided by the change in x. The change in y between points A and B is 20 and the change in x is 4. Dividing these two numbers and we get the gradient of AB to be 5.
We need an equation of a line that is perpendicular to AB, so we do the negative reciprocal of the gradient (this is a rule that you must remember!). In other words, the gradient is ( -1/5). Does this bit make sense?
Now, we know that the gradient of the line is -1/5 or -0.2. We don't, however, know the y-intercept of the line. So we know that the line has the form:
y = -0.2x + c. But, we know that the line passes through point C. So, we can just substitute the co-ordinates of c into our above equation.
We therefore get:
-7 = (-0.2 * -5) + c
-7 = 1 + c
-8 = c
So we now know that the equation of the straight line is y = -0.2x - 8.
But can you see that the question asks for where a and b are integers?
Therefore we have to bring the -0.2x to the other side and multiply both sides by 5 so that we get rid of any fractions.
The final answer is therefore 5y + x = -40.