isabella4martinez
Answered

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

Sagot :

Leora03

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]

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