# Finding slope and intercept of a line, and solving equations

1. Find the slope and intercept for the line 2y-x-4=0

2. Find the slope and intercept for the line 6/9y+2/3x-5=0

3. For the line y= 3x-3 find a line parallel to it that passes through the point (-1,0)

4. For the line y= 2x+2 find a line parallel to it that passes through the points (2,0) (4,4)

5. For the set of points (1,5) and (3,9) find the slope, intercept, and write the equation

6. Solve the equation x squared+4x-12=0 by factoring

7. Solve the equation 4xsquared-25x+36=0 by factoring

8. Solve the equation 4xsquared-2x=0 by factoring

9. Solve the equation 3xsquared-5x-2=0 by using the quadratic equation (DO NOT FACTOR)

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please see the solutions in the attached Word document.

1. Find the slope and intercept for the line 2y-x-4=0

To find the slope and intercept of a line, first put the function into the form:

When this is done, m is the slope and b is the intercept. Now put your line into that form.

Now that this is in the same form as the equation above, it's easy to see that:

Slope =

Intercept =

2. Find the slope and intercept for the line 6/9y+2/3x-5=0

As in problem 1, just rearrange the equation into the form . The slope is and the intercept is .

From this you can see that:

Slope =

Intercept =

3. For the line y= 3x-3 find a line parallel to it that passes through the point (-1,0)

This line is in the , so you can tell immediately that the slope is . Since parallel lines have the same slope, we know that the slope of the line we want is also .

The equation of a line through the point with slope m is:

Substituting , and the point (-1,0) for , you get:

This line has the same slope as the original equation but a different intercept.

4. For the line y= 2x+2 find a line parallel to it that passes through the points (2,0) (4,4)

You can do this problem exactly the same way as problem 3. You can see that the slope is and we'll use the point (4, 4) for . Substituting these into the formula you get:

Again, the parallel line has the same slope but a different intercept. As a check to be sure both points given in the problem are on this line, substitute (2, 0) for .

This confirms that the other point is also on the line.

5. For the set of points (1,5) and (3,9) find the slope, intercept, and write the equation

When two points and are given, you can find the slope with the following formula:

For our two points is (1, 5) and is (3, 9). Substituting into the equation:

Now that we have the slope, we can use one of the points and solve this the same way as the last two problems. Use the slope and use (1, 5) for

This is the equation you are looking for.

Again, as a check, we can plug the other point into this equation.

This shows both points given are on the line.

6. Solve the equation x squared+4x-12=0 by factoring

The solutions for x are -6 and 2.

7. Solve the equation 4xsquared-25x+36=0 by factoring

The solutions for x are 9/4 and 4.

8. Solve the equation 4xsquared-2x=0 by factoring

The solutions for x are 0 and 1/2

9. Solve the equation 3xsquared-5x-2=0 by using the quadratic equation (DO NOT FACTOR)

The solutions for x are -1/3 and 2.

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