Question

write the equation of the line in either form (slope intercept or point slope form) that contains points (4,-5) (8,1)

Answer 1

Answer:

y = $\frac{3}{2}$ x - 11

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, - 5 ) and (x₂, y₂ ) = (8, 1 )

m = $\frac{1-(-5)}{8-4}$ = $\frac{1+5}{4}$ = $\frac{6}{4}$ = $\frac{3}{2}$ , then

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

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

Using (8, 1 ) , then

1 = 12 + c ⇒ c = 1 - 12 = - 11

y = $\frac{3}{2}$ x - 11 ← equation of line in slope- intercept form