Question

Write the equation of a line with the given slope and the given point. Write the equation in slope-intercept form.

y = ?

Answer 1

y = 5/3 x + 3

Explanation:

slope intercept form is y = mx + b

y = y coordinate

m = slope

x = x coordinate

b = y intercept

line equation is y - y1 = m (x - x1)

m = 5/3 (-3,-2)

y - (-2) = 5/3 * (x - (-3) )

y + 2 = 5/3 * (x + 3)

y + 2 = 5/3 x + 5

y = 5/3 x + 3

Answer 2

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

Explanation:

Pre-Solving

We are given that a line has a slope (m) of
`(5)/( 3)`, and contains the point (-3,-2).

We want to write the equation of this line in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept.

Solving

Since we already know the slope of the line, we can immediately plug that into y=mx+b.

Replace m with
`(5)/(3)`

`y = (5)/(3) x + b`

Now, we need to find b.

As the equation passes through (-3,-2), we can use its values to help solve for b.

`-2 =(5)/(3)(-3) + b`

Multiply.

-2 = -5 + b

Add 5 to both sides.

3 = b

Substitute 3 as b in the equation.

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