Question

Use the point–slope formula to write an equation of the line that passes through(-5, -16 )and has a slope of m=3. Write the answer in slope–intercept form (if possible).

Answer 1

Slope-intercept form: y = 3x - 1

Explanation:

We are given that a line passes through the point (-5, -16) and has a slope of 3

We want to write the equation in point-slope form, and simplify it to slope-intercept form (if it is possible to do so).

First, point-slope form is given as
`y-y_1=m(x-x_1)`, where m is the slope and
`(x_1, y_1)` is a point

We have both the slope and a point, but let's label the values of everything to avoid confusion + mistakes:

m = 3

`x_1=-5\\y_1=-16`

Now substitute into the formula (remember: we have NEGATIVE numbers, and the formula uses SUBTRACTION):

`y--16=3(x--5)`

The equation can be simplified

`y+16=3(x+5)`

We can also write this in slope-intercept form

Start by distributing 3 to both x and 5 (multiply both x and 5 by 3)

`y+16=3x + 15`

Subtract 16 from both sides

y = 3x - 1