Question

Input the equation of the given line in slope-intercept form.

The line through (1, 0) and parallel to x - y = 7.

Answer 1

For lines to be parallel, they must have the same slope. We get the slope most easily by rearranging the equation for the line into slope-intercept form:
\[y=mx+b\]If you take your equation, add \(y\) to both sides and subtract 7 from both sides, you'll get that (the y will be on the right side and x on the left, but you can just flop the whole equation around since the two sides are equal).

Next, use the point-slope formula for a line with slope \(m\) through a point \((x_0,y_0)\) to write the new equation:
\[y-y_0=m(x-x_0)\]
and finally rearrange the resulting equation in slope-intercept form as requested by the question.

Answer 2

Thanks for explaining! I actually understand it now! haha thank you!

Answer 3

What's your answer? We'll check the quality of my explanation :-)

Answer 4

I got Y=m(x-1) for the point-slope formula, then converting back to slope-intercept would it be y=mx-1?

Answer 5

If you had \[y-y_0 = m(x-x_0)\]and \[y_0=0, x_0=1\]then\[y-0=m(x-1)\]\[y=mx-m\]after the distributive property. You also need to plug in the value of \(m\) which you know from the first equation...do you remember what it is?