The equation of a line perpendicular to line AB in slope-intercept form is
[tex]y=0.5x+2.5[/tex]
Graph :
- We are given with a graph of a line AB
- Equation of a line perpendicular to AB passes through point (7,6)
From the slope of line AB using any two points from the given line
A is (0,1) and B is (-2,5)
lets find out slope using slope formula
[tex]slope =\frac{y_2-y_1}{x_2-x_1} =\frac{5-1}{-2-0} =-2[/tex]
Slope of perpendicular lines are negative reciprocal of one another
Slope of perpendicular line is [tex]\frac{1}{2}[/tex]
Use point slope formula to find equation of the line
[tex]m=\frac{1}{2} , (7,6)[/tex]
Point slope formula
[tex]y-y_1=m(x-_1)\\y-6=\frac{1}{2} (x-7)\\y-6=0.5x-3.5\\y=0.5x-3.5+6\\y=0.5x+2.5[/tex]
The equation of a line perpendicular to line AB in slope-intercept form is
[tex]y=0.5x+2.5[/tex]
learn more about the perpendicular lines here:
brainly.com/question/2863358
