Equation Help!?

Question

An equation of a line passing through (4, -5) with a slope of 3/7 is:

A.) 3x-7y=47 B.)3x-7y=23 C.) 3x-7y=-47 D.) 3x+7y=2 E.) 3x-7y=-23

How do I do this?

Answer 1

A.

What you want to do first is use the slope-intercept form of the equation for a line. Since you have the coordinates of one point on the line and the slope of the line, that allows you to solve for the y-intercept. Then it is simply a matter of putting the resulting equation in standard form and examining the equation which results and comparing it to your choices listed here.

y = mx + b

Now, plug the values from your point, (4, -5), and the slope, m = 3/7, into the above equation and solve for b.

-5 = 3/7(4) + b
-5 = 12/7 + b
-35/7 - 12/7 = b
-47/7 = b

Since we now have the y-intercept, b = -47/7, we can plug all this into the slope-intercept form of the equation and manipulate it algebraically to obtain the final standard form.

y = (3/7) x - 47/7.

To clear fractions, multiply both sides by 7.

7y = 3x - 47.

Finally, move the constant over to the left side and the y variable to the right side.

47 = 3x - 7y, which we can reflect about the equal sign to obtain:

3x - 7y = 47, which is choice A.

Answer 2

Confirming that the anser is indeed A.