Question

Write an equation for the line parallel to the line -7x - 7y= 7 through the point (-1,2)

Answer 1

`y=-x+1`

Explanation:

Slope-Intercept Formula:

It helps to write the equation in slope-intercept formula to find the slope of an equation in the form:
`y=mx+b` where "m" is the slope of the equation. We can take the equation given:
`-7x-7y=7` and solve for "y" to get the equation in slope-intercept form:

`-7x-7y=7`

add 7x to both sides:

`-7y=7x+7`

Divide both sides by -7

`y=-x-1`

Now in this form we can tell that the coefficient of "x" (the m value) is our slope, which is -1. We need this slope to determine a parallel line as parallel lines share the same slope but different y-intercepts. So a general equation for a parallel line would be:

`y=-x+b\text{ where b }\\e -1`

We're given the point (-1, 2) and we can use it to solve for that "b" value.

We plug in -1 as x and 2 as y

`2=-1(-1)+b\implies 2=1+b\implies 1=b`

Now we just plug this into the general equation to get:
`y=-x+1`