Mathematics: What is the equation that represents the line?

What is the equation that represents the line?

micahatwood03

10.01.2022

see explanation

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 = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, - 6) and (x₂, y₂ ) = (2, - 3) ← 2 points on the line

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

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

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

Using (2, - 3), then

- 3 = $\frac{3}{2}$ + c ⇒ c = - 3 - $\frac{3}{2}$ = - $\frac{9}{2}$

y = $\frac{3}{4}$ x - $\frac{9}{2}$ ← equation of line

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