Question

Find the equation of the line that is parallel to the given line and passes through (5, -1). 32. y = 2x−7

Answer 1

To solve this problem, we need to use our knowledge that parallel lines have the same slope. If we have a line that is parallel to the line y = 2x - 7, our line must also have a slope of 2 (we know this line has a slope of 2 because it is in slope-intercept form, y=mx + b, where m represents slope and b represents the y-intercept).

Now, we can use our known slope and our given point to substitute into point-slope form, as shown below:

y = m (x - h) + k

y = 2 (x - 5) - 1

Next, we can simplify our equation by using the distributive property to get rid of the parentheses.

y = 2x - 10 - 1

Finally, we can complete our equation by computing the subtraction.

y = 2x - 11

We can conclude that this is the correct answer because if you plug in the point (5, -1) you get a true statement and it has a slope of 2.

Therefore, the answer is y = 2x - 11.

Hope this helps!