Question

A coordinate plane with a line passing through the points (0, negative 4) and (2, 2). What is the equation of the graphed line written in standard form?

Answer 1

Answer:

3x - y = 4

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

First find the equation in slope- intercept form

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 ) = (0, - 4) and (x₂, y₂ ) = (2, 2)

m = $\frac{2+4}{2-0}$ = $\frac{6}{2}$ = 3

Note the line crosses the y- axis at (0, - 4) ⇒ c = - 4

y = 3x - 4 ← in slope- intercept form

Add 4 to both sides

y + 4 = 3x ( subtract y from both sides )

4 = 3x - y, that is

3x - y = 4 ← in standard form