Question

Write an equation for the graph below in point-slope form and then solve rewrite in slope-intercept form.

Answer 1

We are given the graph of a line and we are asked to determine its equation in point-slope form.

The general form in slope point form of a line is:

`y-y_0=m(x-x_0)`

Where:

`\begin{gathered} m=\text{ slope} \\ (x_0,y_0)\text{ is apoint in the line} \end{gathered}`

to determine the slope we will use the following formula:

`m=(y_2-y_1)/(x_2-x_1)`

Where:

`(x_1,y_1);(x_2,y_2)=\text{ points on the line}`

We will choose two points on the line from the graph:

`\begin{gathered} (x_1,y_1)=(0,1) \\ (x_2,y_2)=(2,2) \end{gathered}`

Now, we plug in the values in the formula for the slope:

`m=(2-1)/(2-0)=(1)/(2)`

Now, we substitute the value of the slope in the equation of the line:

`y-y_0=(1)/(2)(x-x_0)`

Now, we plug in the first point we choose for the line:

`\begin{gathered} y-1=(1)/(2)(x-0) \\ \\ y-1=(1)/(2)x \end{gathered}`

And thus we have determined the equation of the line in point-slope form.

The slope-intercept form is the following:

`y=mx+b`

To convert this equation to slope-intercept form, we will take the previous equations and we will add 1 to both sides:

`y=(1)/(2)x+1`

And thus we have determined the slope-intercept form of the equations of the line.