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:

y = x + 1

Step-by-step explanation:

Step 1: Find the slope.

Parallel lines have the same slope. That means that the line we are seeking is going to have the same slope as line x - y = 7.

To find the slope of the line x - y = 7 let's change it to the slope-intercept form.

Slope-Intercept Form

y = mx + b

m ... slope

b ... y-intercept

Let's change the equation of the parallel line to slope-intercept form (isolate y).

x - y = 7

Add y on both sides.

x - y + y = 7 + y

x = 7 + y

Subtract 7 on both sides.

x - 7 = 7 + y - 7

x - 7 = y

y = x - 7

Let's read the slope from the equation.

Instead of y = x - 7 we can write y = 1x -7.

Now it's obvious that m (slope) is 1.

m = 1

So far, our equation of the line is:

y = 1x + b

which is te same as

y = x + b

Step 2: Find y-intercept.

To find out y-intercept (b), we substitiute the point (-7, -6) in the equation. Points are in form (x, y) so -7 is x and -6 is y.

y = x + b

-6 = -7 + b

Solve for b.

1 = b

Step 3: Substitute slope and y-intercept in general formula for slope-intercept form of the line.

Now substitute m and b in slope-intercept form y = mx + b.

m = 1

b = 1

Equation of the line:

y = x + 1