We know perpendicular slopes have negative reciprocal slopes.
If Line 1 has slope
[tex]m[/tex]
The perpendicular line, Line 2, will have slope
[tex]-\frac{1}{m}[/tex]
The slope-intercept form of a line is given by,
[tex]y=mx+b[/tex]
Where
m is the slope
b is the y-intercept
The line shown is,
[tex]y=-2x+1[/tex]
So,
Slope = - 2
Y-intercept = 1
Since this line has slope of "-2", the perpendicular line to this will have a slope of,
[tex]-\frac{1}{-2}=\frac{1}{2}[/tex]
So, it's slope intercept form of the equation will be:
[tex]y=\frac{1}{2}x+b[/tex]
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:
[tex]\begin{gathered} y=\frac{1}{2}x+b \\ 3=\frac{1}{2}(2)+b \\ 3=1+b \\ b=3-1 \\ b=2 \end{gathered}[/tex]Thus, the
equation of the line is[tex]y=\frac{1}{2}x+2[/tex]
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:
[tex]\begin{gathered} y=\frac{1}{2}x+2 \\ 0=\frac{1}{2}x+2 \\ \frac{1}{2}x=-2 \\ x=\frac{-2}{\frac{1}{2}}=-2\times\frac{2}{1}=-4 \end{gathered}[/tex]
So, the x-intercept is (-4,0)
Secondly, the y-intercept:
[tex]\begin{gathered} y=\frac{1}{2}x+2 \\ y=\frac{1}{2}(0)+2_{} \\ y=2 \end{gathered}[/tex]
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:
