Question

What is the equation of the line that passes through (4, -1) and (-2, 3)?

Answer 1

Answer:

A

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, - 1) and (x₂, y₂ ) = (- 2, 3)

m = $\frac{3+1}{-2-4}$ = $\frac{4}{-6}$ = - $\frac{2}{3}$ , thus

y = - $\frac{2}{3}$ x + c ← is the partial equation

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

Using (- 2, 3) , then

3 = $\frac{4}{3}$ + c ⇒ c = 3 - $\frac{4}{3}$ = $\frac{5}{3}$

y = - $\frac{2}{3}$ x + $\frac{5}{3}$ ← in slope- intercept form

Multiply through by 3 to clear the fractions

3y = - 2x + 5 ( add 2x to both sides )

2x + 3y = 5 ( subtract 5 from both sides )

2x + 3y - 5 = 0 ← in general form