Question

Write the equation of the line in slope-intercept form that passes through (-7,-6) and (10,8)

Answer 1

The line is graphically represented based on the affine function y = mx + b, in which m represents the slope, b the y-intercept, x and y the coordinates of a point.
Let A(-7,-6) and B(10,8).
The Slope can be found by dividing the subtraction of yB and yA by the subtraction of xB and xA. So m = (yB-yA)/(xB-xA): The point with the bigger X always comes first.
By hypothesis, yB = 8 and yA = -6 so yB - yA = 8 - (-6) = 8 + 6 = 14
And xB = 10 and xA = -7 so xB - xA = 10 - (-7) = 10 + 7 = 17
So m = (yB-yA)/(xB-xA) = 14/17

So the equation of the line becomes y = 14/17x + b.
Since x and y represents the coordinates of a point, let's use the coordinates of B(10,8) to find the y-intercept b.
y = 14/17x + b
8 = 14/17 * 10 + b
8 = 140/17 + b
b = 8 - 140/17
b = -4/17

So the equation of the line is y = 14/17x - 4/17

I've added the graphical representation of the line in a picture under the answer.

Hope this Helps! :)