The slope of a line that is perpendicular to the line
shown in the graph is = 4
Hence, option 'd' is true.
Step-by-step explanation:
From the line equation, let us take two points
(0, 2)(4, 1)
Finding the slope between two points
![\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](/tpl/images/0945/2101/e11e5.png)
![\left(x_1,\:y_1\right)=\left(0,\:2\right),\:\left(x_2,\:y_2\right)=\left(4,\:1\right)](/tpl/images/0945/2101/91e0f.png)
![m=\frac{1-2}{4-0}](/tpl/images/0945/2101/cf1fc.png)
![m=-\frac{1}{4}](/tpl/images/0945/2101/3d7a7.png)
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so
The slope of the perpendicular line will be:
![-\frac{1}{-\frac{1}{4}}=4](/tpl/images/0945/2101/719a0.png)
Thus, the slope of a line that is perpendicular to the line
shown in the graph is = 4
Hence, option 'd' is true.