Question

Write an equation for the line that passes through the points (-8,5) and (-2,9) in slope-intercept form.

Answer 1

Answer:

y = $\frac{2}{3}$ x + $\frac{31}{3}$

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 8, 5) and (x₂, y₂ ) = (- 2, 9)

m = $\frac{9-5}{-2+8}$ = $\frac{4}{6}$ = $\frac{2}{3}$ , thus

y = $\frac{2}{3}$ x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 2, 9 ), then

9 = - $\frac{4}{3}$ + c ⇒ c = 9 + $\frac{4}{3}$ = $\frac{31}{3}$

y = $\frac{2}{3}$ x + $\frac{31}{3}$ ← equation of line