Question

Write an equation of the line passing through each of the following pairs of points. a (−10, 4), (2, −5)

Answer 1

Answer:

see explanation

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 = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 10, 4) and (x₂, y₂ ) = (2, - 5)

m = $\frac{-5-4}{2+10}$ = $\frac{-9}{12}$ = - $\frac{3}{4}$, thus

y = - $\frac{3}{4}$ x + c ← is the partial equation of the line

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

Using (2, - 5), then

- 5 = - $\frac{3}{2}$ + c ⇒ c = - 5 + $\frac{3}{2}$ = - $\frac{7}{2}$

y = - $\frac{3}{4}$ x - $\frac{7}{2}$ ← equation of line