Answer:
[tex]d = \frac{5}{3} [/tex]
Step-by-step explanation:
In the slope- intercept form (y= mx +c), the coefficient of x is the slope of the graph.
y= 3x +4
Slope of given line= 3
[tex]\boxed{slope = \frac{y1 - y2}{x1 - x2} }[/tex]
The product of the slopes of perpendicular lines is -1.
[tex] (3)[ \frac{d - 4}{5 - ( - 2)} ] = - 1[/tex]
Divide both sides by 3:
[tex] \frac{d - 4}{5 + 2} = \frac{ - 1}{3} [/tex]
[tex] \frac{d - 4}{7} = \frac{ - 1}{3} [/tex]
Cross multiply:
3(d -4)= -1(7)
Expand:
3d -12= -7
Add 12 on both sides:
3d= 12 -7
3d= 5
Divide both sides by 3:
[tex]d = \frac{5}{3} [/tex]
