Question

Graph the points (-3,4) and (1,1). If you drew a line through the points, name three other points that would be on the line. How did you find them?

Answer 1

The easiest way to solve this problem is to find the equation of the line joining these two points, then get the values of the points on this line.

We have first point (x1,y1) = (-3,4) and second point (x2,y2) = (1,1).
The equation of the line is y = mx + c
The slope (m) = (y2-y1) / (x2-x1) = (1-4) / (1--3) = -0.75

Then we will use one of these points to get the value of c as follows:
y = mx + c
1 = -0.75 (1) + c ..............> c = 1.75

The equation of this straight line is:
y = -0.75 x + 1.75

Now to get points on this line, we will assume values for either x or y and calculate the other as follows:
1- For x = 0:
y = -0.75 (0) + 1.75 = 1.75
point is (0,1.75)
2- For y = 0:
0 = -0.75 x + 1.75 ..............> x = 2.334
point is (2.334,0)
3- For x = 2:
y = -0.75(2) + 1.75 = 0.25
point is (2,0.25)