Answer:
y = x + 1
Step-by-step explanation:
Step 1: Find the slope.
<u>Parallel lines have the same slope.</u> 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.
<u>Slope-Intercept Form</u>
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
