Write an equation of the line passing through the point -7, 3 that is parallel to the line y=x-3 .

Answer 1

Hi, Natalie!

The first key to answering a question like this is to note that there are two main things that we need to write an equation of a line in the form y = mx + b: we need the slope (m) and the y-intercept (b).

We can find the slope first by noting that lines that are parallel to one another have the same slope.

We are given the line y = x + 3 --> in this case, our slope is m = 1. Therefore, the slope of our parallel line must also be m = 1.

Next, we need to calculate b. We know our slope is 1, so the equation of our new line must be of the form: y = (1)x + b --> y = x + b. Finally, we are given that the line passes through the point (-7, 3). We can substitute the x and y values from this point into our equation to solve for b:

y = x + b

(3) = (-7) + b

b = 10

Now that we have m = 1 and b = 10, we just need to substitute them into our general equation for a line, y = mx + b:

y = mx + b

y = (1)x + (10)

y = x + 10

I hope that this answer was helpful, and please don't hesitate to reach out if you have any further questions!