Question

What is an equation of the line that goes through (4, 5) and (-3, -2)? *

y = x + 1
y = 3/7x - 1
y = -x - 1
y = 7/3x + 2

Answer 1

y = x + 1

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 ) = (4, 5 ) and (x₂, y₂ ) = (- 3, - 2 )

m =
`(-2-5)/(-3-4)` =
`(-7)/(-7)` = 1 , then

y = x + c ← is the partial equation

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

Using (4, 5 ) , then

5 = 4 + c ⇒ c = 5 - 4 = 1

y = x + 1 ← equation of line