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

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 =

with (x₁, y₁ ) = (- 3, 7) and (x₂, y₂ ) = (9, - 1)

m = = = = - , then

y = - 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 = - x + 5 ← equation of line

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.