Question

Which of the following equations represents the line that passes throught the points (2, -6) and(-4,3)?A.y= -3/2x - 7B.y= -2/3x - 3C.y= -2/3x + 1/3D.y= -3/2x - 3

Answer 1

Given two points (x1, y1) and (x2, y2), the slope (m) is computed as follows:

`m=(y_2-y_1)/(x_2-x_1)`

Replacing with points (2, -6) and (-4, 3), we get:

`m\text{ = }(3-(-6))/(-4-2)=(9)/(-6)=-(3)/(2)`

slope-intercept form of a line:

y = mx + b

where m is the slope and b is the y-intercept.

Replacing with point (2, -6) and m = -3/2, we get:

-6 = -3/2(2) + b

-6 = -3 + b

-6 + 3 = b

-3 = b

Finally, the equation is:

y = -3/2x - 3