Question

Find the equation of a line parallel to y = 3x - 4 that passes through (-2,2).
First identify the slope of y = 3x - 4.
What will be the slope of the new line?

Answer 1

Answer:

Slope: 3.

Equation: y = 3x + 8.

Step-by-step explanation:

Lines that are parallel to each other will have the same slopes.

So, the slope of the new line will be 3.

Since we have the slope, and a set of coordinates the line passes through, we can find the equation. So far, we have y = 3x + b. x = -2, y = 2.

2 = 3(-2) + b

3(-2) + b = 2

-6 + b = 2

b = 8

So, the equation of the line will be y = 3x + 8.

Hope this helps!

Answer 2

Parallel lines have the same slope

The equation of the new line is $\mathbf{y = 3x+8}$

The equation is given as:

$\mathbf{y = 3x - 4}$

A linear equation is represented as:

$\mathbf{y = mx + b}$

Where m represents the slope.

So, by comparison:

$\mathbf{m = 3}$

This means that the slope of the new line is 3

So, the equation is calculated as:

$\mathbf{y = m(x -x_1) + y_1}$

This gives

$\mathbf{y = 3(x --2) + 2}$

$\mathbf{y = 3(x+2) + 2}$

$\mathbf{y = 3x+6 + 2}$

$\mathbf{y = 3x+8}$

Hence, the equation of the new line is $\mathbf{y = 3x+8}$

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