Question

If the line through (- 2,4)and (5, d)is perpendicular to the graph of y = 3x + 4.Find the value of d.

Answer 1

Answer:

$d = \frac{5}{3}$

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

$\boxed{slope = \frac{y1 - y2}{x1 - x2} }$

The product of the slopes of perpendicular lines is -1.

$(3)[ \frac{d - 4}{5 - ( - 2)} ] = - 1$

Divide both sides by 3:

$\frac{d - 4}{5 + 2} = \frac{ - 1}{3}$

$\frac{d - 4}{7} = \frac{ - 1}{3}$

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:

$d = \frac{5}{3}$