Question

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

a.) 2 x + 3 y - 5 = 0
b.) -2 x + 3 y - 5 = 0
c.) 2 x - 3 y - 5 = 0

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

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 ( subtract - 2x + 5 from both sides )

2x + 3y - 5 = 0 ← in general form