Select the equations of the lines that are parallel to the line whose equation is y= 3x +5?
6x + 2y = 12, -3x + y = 8, 3y = 9x, y = -1/3x

Solution:

The standard slope-intercept form for an equation of a line is

y = mx + b

Where m is the slope

So the slope of given line y = 3x + 5 is 3

The lines which are parallel to the line whose equation is y = 3x + 5 must have the same slope as this line. Let us consider each equation to check.

1. 6x + 2y = 12

Divide the entire equation by 2

3x + y = 6

y = - 3x + 6

Slope = - 3

2. - 3x + y = 8

It can be written as

y = 3x + 8

Slope = 3

3. 3y = 9x

y = 3x

Slope = 3

4. y = -1/3 x

Slope = -1/3

Therefore, the equations are - 3x + y = 8 and 3y = 9x.

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Select the equations of the lines that are parallel to the line whose equation is y= 3x +5?
6x + 2y = 12, -3x + y = 8, 3y = 9x, y = -1/3x

Summary:

The equations of the lines that are parallel to the line whose equation is y= 3x +5 are - 3x + y = 8 and 3y = 9x.