Question

What is an equation of the line that passes through the point (-7, -6) and is parallel to the line x-y=7?

Answer 1

Answer:

Step-by-step explanation:

For two lines to be parallel their slopes must be equal. For two lines to be perpendicular their slopes must be the negative reciprocal of each other.

Step 1 Find the slope of the equation.

Put it into the slope-intercept form. y = mx + b.  

For x-y = 7, move the x to the left; therefore subtract the x from both sides. this leaves you  -y = -x + 7

Then, divide both sides by -1 to get a positive y.  -y/-1 = (-x + 7)/-1

This leaves y = x - 7  The slope(m) for this equation is m = 1

The other equation must also have a slope of 1 or m=1 for the lines to be parallel.

Use the point given to you (-7, -6) and substitute for (x, y)

The slope-intercept form y = mx + b can once again be used.

x = -7, y =-6, and slope or m = 1

Therefore,  y = mx + b substituted will be -6 = (1)(-7) + b; now, solve for b which is the y intercept

-6 = -7 + b add 7 to both sides -6 +7 = -7 + b +7 ; therefore, b = 1

Now you know the slope(m) which is equal to 1 and the y-intercept(b) which is equal to 1.

Finally, substitute the m and b in the slope-intercept form

            y = (1)x + 1 or y = x +1