Question

what is the slope- intercept form of the equation of the line that passes through the points (-3,2) and(1,5)

Answer 1

Answer:

y = $\frac{3}{4}$ x + $\frac{17}{4}$

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 )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (1, 5)

m = $\frac{5-2}{1+3}$ = $\frac{3}{4}$, hence

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

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

using (1, 5 ), then

5 = $\frac{3}{4}$ + c ⇒ c = 5 - $\frac{3}{4}$ = $\frac{17}{4}$

y = $\frac{3}{4}$ x + $\frac{17}{4}$ ← in slope-intercept form