Answer:
The gradient of line perpendicular to AB is: m = [tex]\frac{1}{2}[/tex]
The equation of line passing through point A and perpendicular to AB is [tex]\mathbf{y=\frac{1}{2}x+6}[/tex]
Step-by-step explanation:
The line on the graph passes through the points A (0,6) and B (3,0)
b) Find the gradient of a line perpendicular to AB
First we will find gradient (slope) of AB
The formula used to find Slope is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We have [tex]x_1=0, y_1=6, x_2=3, y_2=0[/tex]
Putting values and finding slope:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{0-6}{3-0}\\Slope=\frac{-6}{3}\\Slope=-2[/tex]
So, we get slope: m = -2
Now, the gradient of line perpendicular to AB will be opposite to the slope of AB
The gradient of line perpendicular to AB is: m = [tex]\frac{1}{2}[/tex]
c) Find the equation of line passing through point A and perpendicular to AB
The equation of line can be found using slope m = [tex]\frac{1}{2}[/tex] and y-intercept b
We need to find y-intercept b:
Using slope m = [tex]\frac{1}{2}[/tex] and point A (0,6)
y=mx+b
6= [tex]\frac{1}{2}[/tex] (0)+b
6=0+b
b=6
So, y-intercept is b =6
So, Equation of line with slope m = [tex]\frac{1}{2}[/tex] and y-intercept b =6 is:
[tex]y=mx+b\\y=\frac{1}{2}x+6[/tex]
So, The equation of line passing through point A and perpendicular to AB is [tex]\mathbf{y=\frac{1}{2}x+6}[/tex]
