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

`d = (5)/(3)`

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 = (y1 - y2)/(x1 - x2) }`

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

`(3)[ (d - 4)/(5 - ( - 2)) ] = - 1`

Divide both sides by 3:

`(d - 4)/(5 + 2) = ( - 1)/(3)`

`(d - 4)/(7) = ( - 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 = (5)/(3)`