Question

Hello! I already solved the slope intercept equation part I just have trouble graphing and making the two points intersect because it is perpendicular.

Answer 1

We know perpendicular slopes have negative reciprocal slopes.

If Line 1 has slope

`m`

The perpendicular line, Line 2, will have slope

`-(1)/(m)`

The slope-intercept form of a line is given by,

`y=mx+b`

Where

m is the slope

b is the y-intercept

The line shown is,

`y=-2x+1`

So,

Slope = - 2

Y-intercept = 1

Since this line has slope of "-2", the perpendicular line to this will have a slope of,

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

So, it's slope intercept form of the equation will be:

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

This line passes through the point (x, y) = (2, 3), so, substituting these values in the respective variables, we can solve for "b", the y-intercept. Shown below:

`\begin{gathered} y=(1)/(2)x+b \\ 3=(1)/(2)(2)+b \\ 3=1+b \\ b=3-1 \\ b=2 \end{gathered}`Thus, the equation of the line is
`y=(1)/(2)x+2`

To graph this line, we will find 2 points (x-intercept and y-intercept).

• To find the ,x-intercept,, we put ,y = 0,.

,

• To find the ,y-intercept,, we put ,x = 0,.

First, the x-intercept:

`\begin{gathered} y=(1)/(2)x+2 \\ 0=(1)/(2)x+2 \\ (1)/(2)x=-2 \\ x=(-2)/((1)/(2))=-2*(2)/(1)=-4 \end{gathered}`

So, the x-intercept is (-4,0)

Secondly, the y-intercept:

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

So, the y-intercept is (0, 2).

Now, we can draw the two coordinates >>>>

(-4, 0)

and

(0, 2)

and draw a straight line that passes through these 2 points.

Let's graph the line: