0

# Can you find the equation of a line if you are given the slope and the x-intercept? Why or why not?

Hi,

I wanted to double check my answer before I turned in this assignment. I answered this question as follows: No, because in order to find the equation of a line you must be given not only the slope, but also the point on a line, which includes the y-intercept. Is my answer correct/justifiable?

Any help is appreciated!

### 1 Answer by Expert Tutors

PIYUSH L. | Maths tutoring for middle school to college maths studentsMaths tutoring for middle school to coll...
5.0 5.0 (6 lesson ratings) (6)
0
Hi Rachel,

Equation of a line can be written by y = mx + c     where m is slope and c is intercept on y axis.

Now in the question we are given the slope and x intercept ( I am assuming we know whether the intercept is positive or negative). The y coordinate will be zero for the point where the line cuts x axis.

Just for example it is given the slope of line is 4 and x intercept is +1.

Now using this information and the basic line equation we have,

0 = 4*1+c
c = -4

Therefore equation of line will be y= 4x-4

So we can find out the equation of the line if we know the slope and the x intercept along with its sign(positive or negative). If we don't know the sign of x intercept, there will be 2 possible solutions to the problem.

If you do not have the sign in any problem is almost impossible to solve it.
I guess I'm a little confused by all of the theoretical stuff here.

Rachel said, right up front: "in order to find the equation of a line you must be given not only the slope, but also the point on a line." That part, I agree with. But then, you said "which includes the y-intercept."  I'm not sure what that means.

Yes, you need a point on the line.  Why does the point I give you haaaaave to be the y-intercept?

Try this:

- Pick any old point on the x axis.  That's your x intercept.
- Make up a slope.

Given those two pieces of information, can you draw the line?  If you can, then that's enough to write the equation of the line you've drawn.  Maybe you don't have the y-intercept directly, but maybe given those two pieces of information, you could figure it out...  (and that's what piyush showed how to do)