Question

What is an equation of the line that passes through the points (6, 8) and (-3, 2)?

Answer 1

Answer:

y = $\frac{2}{3}$ x + 4

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 ) = (6, 8) and (x₂, y₂ ) = (- 3, 2)

m = $\frac{2-8}{-3-6}$ = $\frac{-6}{-9}$ = $\frac{2}{3}$ , 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 (6, 8), then

8 = 4 + c ⇒ c = 8 - 4 = 4

y= $\frac{2}{3}$ x + 4 ← equation of line