Question

the slope and one point on the line is given: m = 4 and (-1,0). use the point slope form to fine the equation of that line. then write the equation in slope-intercept form. what is the y-intercept?

Answer 1

- The Slope-Intercept form of the equation of a line is:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

- The Point-Slope form of the equation of a line is:

`y-y_1=m(x-x_1)`

Where "m" is the slope and this is a point on the line:

`(x_1,y_1)`

You know that (according to the information given in the exercise):

`\begin{gathered} m=4 \\ x_1=-1 \\ y_1=0 \end{gathered}`

Then, you can determine that the equation of that line in Point-Slope form is:

`\begin{gathered} y-0=4(x-(-1)) \\ y=4(x+1) \end{gathered}`

In order to write it in Slope-Intercept form, you only need to simplify the right side of the equation applying the Distributive property. Then, you get:

`\begin{gathered} y=(4)(x)+(4)(1) \\ y=4x+4 \end{gathered}`

You can identify that:

`b=4`

Then, the answers are:

- Equation in Point-Slope form

`y=4(x+1)`

- Equation in Slope-Intercept form

`y=4x+4`

- The y-intercept

`b=4`