Question

How to find the equation of this line?

Answer 1

Answer:

y = - $\frac{6}{7}$ x - $\frac{10}{7}$

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 ) = (- 4, 2 ) and (x₂, y₂ ) = (3, - 4) ← 2 points on the line

m = $\frac{-4-2}{3+4}$ = - $\frac{6}{7}$ , thus

y = - $\frac{6}{7}$ x + c ← is the partial equation

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

Using (- 4, 2 ), then

2 = $\frac{24}{7}$ + c ⇒ c = 2 - $\frac{24}{7}$ = - $\frac{10}{7}$

y = - $\frac{6}{7}$ x - $\frac{10}{7}$ ← equation of line