Write an equation in slope-intercept form for the line passing through the pair of points. (6, 4) (4, -5)

Question

Write an equation in slope-intercept form for the line passing through the pair of points. (6, 4) (4, -5)

Answer 1

Given two points (x_1,y₁) and (x₂,y₂), an equation for the line passing through them may be computes as

y= m(x-x₁) + y₁, where m = (y₂-y₁)/(x₂-x₁). In this case, we get m = (-5-4)/(4-6) = -9/-2 = 9/2. So

y= 9/2(x-6) + 4

= 9x/2 -6(9/2) + 4

= 9x/2 -23.

This is the slope-intercept form. The slope is 9/2 and the y-intercept is -23.