A given line has the equation 10x+2y=-2. What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?
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y=-5x+12
5x+y=12
y-12=5(x-0)
5x+y=-1
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Step-by-step explanation:

Given

Required

Equation of line parallel to the above that passes through (0,12)

The first thing is to get the slope of the first line

Subtract 10x from both sides

Divide through by 2

Using the general form of a line equation

By comparison;

The condition for parallel line is that

This means that the slope of the second line is -5

Now, the equation of the line can be calculated using the following formula

So, becomes

Multiply both sides by x

Add 12 to both sides

The equation of the line in slope intercept form is