Question

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)?

Answer 1

y = -5x + 12 since the slope of that line is -5x and in order to pass through that point the y intercept must be 12

Answer 2

Step 1

Find the slope of the given line

we have

$10x+2y=-2$

Isolate the variable y

Subtract $10x$ both sides

$2y=-10x-2$

Divide by $2$ both sides

$y=-5x-1$

The slope of the given line is

$m=-5$

Step 2

Find the equation of the line that is parallel to the given line and passes through the point $(0, 12)$

we know that

If two lines are parallel. then their slope are equal

In this problem we have

$m=-5$

$(0, 12)$

The equation of the line into slope-intercept form is equal to

$y=mx+b$

substitute the values

$12=-5*0+b$

$b=12$

the equation of the line is

$y=-5x+12$

therefore

the answer is

$y=-5x+12$