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

$b=4$