Question

What is the equation of the line that passes through the points (-2, 1) and (6, 3)?

Answer 1

Answer:

y = $\frac{1}{4}$ x + $\frac{3}{2}$

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 ) = (- 2, 1 ) and (x₂, y₂ ) = (6, 3 )

m = $\frac{3-1}{6-(-2)}$ = $\frac{2}{6+2}$ = $\frac{2}{8}$ = $\frac{1}{4}$ , then

y = $\frac{1}{4}$ x + c ← is the partial equation

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

using (6, 3 ) , then

3 = $\frac{3}{2}$ + c ⇒ c = 3 - $\frac{3}{2}$ = $\frac{3}{2}$

y = $\frac{1}{4}$ x + $\frac{3}{2}$ ← equation of line