find the equation of a line that passes through the points (3,7) and (5,3). Leave your answer in the form y=mx+c

y = - 2x + 13

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 ) = (5, 3)

m = = = - 2, thus

y = - 2x + c ← is the partial equation

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

Using (3, 7), then

7 = - 6 + c ⇒ c = 7 + 6 = 13

y = - 2x + 13 ← equation of line

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is