Question

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​

Answer 1

y = - 2x + 13

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 =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (3, 7) and (x₂, y₂ ) = (5, 3)

m =
`(3-7)/(5-3)` =
`(-4)/(2)` = - 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