Answer:
[tex]y = - \frac{4}{3}x + 1[/tex]
Step-by-step explanation:
Slope-intercept form
y= mx +c, where m is the slope and c is the y-intercept.
y= ¾x -1
Slope= ¾
The product of the slopes of perpendicular lines is -1.
Let the slope of the line be m.
m(¾)= -1
m= -1 ÷¾
[tex]m = - \frac{4}{3} [/tex]
[tex]y = - \frac{4}{3} x + c[/tex]
To find the value of the y-intercept, substitute a pair of coordinates into the equation.
When x= 3, y= -3,
[tex] - 3 = - \frac{4}{3} (3) + c[/tex]
[tex] - 3 = - 4 + c[/tex]
c= 4 -3
c= 1
Thus, the equation of the line is [tex]y = - \frac{4}{3} x + 1[/tex].
