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3 years ago

what is the equation of the line that is parallel to the line y= 3x-4 and passes through the point (4, -2)

Mathematics

1 answer:

Nimfa-mama [501]3 years ago

5 0

Answer:

y = 3x - 14

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 4 is in this form with slope m = 3

• Parallel lines have equal slopes, hence

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (4, - 2) into the partial equation

- 2 = 12 + c ⇒ c = - 2 - 12 = - 14

y = 3x - 14 ← equation of parallel line

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2 years ago

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To find:

The average rate of change.

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Average rate of change formula:

$$\frac{f(b)-f(a)}{b-a}$

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Substitute x = 4 and x = 2 in f(x).

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Average rate of change from 2 to 4 is 12.

(b) Average rate of change from 1 to 3:

Substitute x = 3 and x = 1 in f(x).

$$\frac{f(3)-f(1)}{3-1}=\frac{(2(3)^2+6)-(2(1)^2+6)}{3-1}$

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Average rate of change from 2 to 4 is 8.

(c) Average rate of change from -2 to 1:

Substitute x = 1 and x = -2 in f(x).

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