Question

Find the slope and y-intercept of the line that is parallel to y=3x-3 and passes through the point (-2,7)

Answer 1

A line that is parallel to that line and hits (-2, 7) is y = 3x + 13.

The first thing we have to note is that it will have the same slope. Since the coefficient of x is 3, we know the slope is also 3. This means the new line will have that slope (this is the definition of parallel lines).

Now we can use slope intercept form, the slope and a point to find the y intercept (b).

y = mx + b

7 = 3(-2) + b

7 = -6 + b

13 = b

Now we use the slope we found (3) and the intercept (13) and place them in the final equation.

y = 3x + 13