Question

Which equation represents the line that passes through the points (–3, 7) and (9, –1)?
y = negative two-thirds x + 5
y = negative two-thirds x minus 7
y = two-thirds x minus 7
y = two-thirds x + 5

Answer 1

Answer:

1st option

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 ) = (- 3, 7) and (x₂, y₂ ) = (9, - 1)

m = $\frac{-1-7}{9-(-3)}$ = $\frac{-8}{9+3}$ = $\frac{-8}{12}$ = - $\frac{2}{3}$ , 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 (9, - 1 ) , then

- 1 = - 6 + c ⇒ c = - 1 + 6 = 5

y = - $\frac{2}{3}$ x + 5 ← equation of line