Question

Which is an equation in point-slope form of the line that passes through the points (4, 5) and (-3, - 1)? A. y-1 = 6/7 (x-3) B. y+3 = 7/6 (x+1) C. y+1 = 6/5 (x+3) D. y+1 = 6/7 (2+3)

Answer 1

The form of the slope-point of the linear equation is

y - y1 = m(x - x1)

m is the slope of the line

(x1, y1) is a point on the line

The rule of the slope is

$m=\frac{y2-y1}{x2-x1}$

(x1, y1) and (x2, y2) are two points on the line

The line passes through points (4, 5) and (-3, -1)

x1 = 4 and y = 5

x2 = -3 and y2 = -1

Substitute them in the rule of the slope to find it

$m=\frac{-1-5}{-3-4}=\frac{-6}{-7}=\frac{6}{7}$

Let us substitute it in the form of the equation above and use point (-3, -1)

$\begin{gathered} y-(-1)=\frac{6}{7}(x--3) \\ y+1=\frac{6}{7}(x+3) \end{gathered}$

The answer is D