Question

What is the equation of the line that passes through the point (-5,2) and has a slope of 4/5

Answer 1

Below.

Explanation:

Use the point-slope form of a straight line.

y - y1 = m(x - x1)

Here m = 4/5, x1 = -5 and y1 = 2, so

y - 2 = 4/5(x - -5))

y - 2 = 4/5 x + 4

y = 4/5x + 6 is the answer in slope-intercept form.

Standard form:

Multiply through by 5:

5y = 4x + 30

4x - 5y = -30 is the answer in standard form.

Answer 2

y =
`(4)/(5)` x + 6

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m =
`(4)/(5)` , then

y =
`(4)/(5)` x + c ← is the partial equation

To find c substitute (- 5, 2 ) into the partial equation

2 = - 4 + c ⇒ c = 2 + 4 = 6

y =
`(4)/(5)` x + 6 ← equation of line