A line passes through the point  and has a slope of  . Write an equation for this line.

Expert Answers
embizze eNotes educator| Certified Educator

Your question did not include the point or slope, but here is the general method:

Given a point `(x_1,y_1)` and a slope m, the equation of the line can be found from the slope formula.

Consider a general point on the graph (x,y) and the given point `(x_1,y_1)` . From the slope formula we have:

`m=(y-y_1)/(x-x_1)`  Multiplying both sides we get:

`y-y_1=m(x-x_1)`  which is the point-slope form of a line.

For example: given (2,3) and slope 5:

y-3=5(x-2) is the equation of the line through the point with slope 5. We can rewrite this in slope-intercept form:

y=5x-10+3 or y=5x-7.


Another approach is to realize that you have a particular point and the slope, so you can solve for the y-intercept. Again using (2,3) and slope 5:

We know the answer will be in the form y=mx+b. Substituting the known values we get:

3=5(2)+b ==> b=-7 so y=5x-7.