Question

Find the equation for the line below.

Answer 1

Answer:

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

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 ) = (- 6, - 5) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = $\frac{1-(-5)}{2-(-6)}$ = $\frac{1+5}{2+6}$ = $\frac{6}{8}$ = $\frac{3}{4}$ , then

y = $\frac{3}{4}$ x + c ← is the partial equation

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

Using (2, 1 ) , then

1 = $\frac{3}{2}$ + c ⇒ c = 1 - $\frac{3}{2}$ = $\frac{2}{2}$ - $\frac{3}{2}$ = - $\frac{1}{2}$

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