What if the equation is not in slope-intercept form?

Ax + By = C

This part of the resource will show you how to manipulate the equation so you can use the graphing calculator to check your answer.

Forms of Linear Equations

To change a standard form equation to a slope-intercept form, you must isolate the variable y on the left side of the equation.

You can review the steps to change an equation from standard form to slope-intercept form in these 2 examples.

The following is a typical question you might see that has answer choices in standard form.

Which equation best describes the graph shown below?

x − 2y = 14 x − 2y = −14 x + 2y = 14 x + 2y = −14

Solving each equation for y, the equations are:

1. y = 1 over 2 1 2 x – 7


2. y = 1 over 2 1 2 x + 7   y-intercept of 7 and slope of 1 over 2 1 2


3. y = 1 over 2 - 1 2 x + 7


4. y = 1 over 2 - 1 2 x – 7

To see how x − 2y = −14 was converted to y = 1 over 2 1 2 x + 7, watch the following presentation.

How can you check that y = 1 over 2 1 2 x + 7 is the same equation as x − 2y = −14?

Calculator!

I think the right equation is y = 1 over 2 1 2 x + 7.

According to this, the points (0, 7), (2, 8) (4, 9) and (6, 10) should all be points on the graph. Substitute the x- and y-values from these points into x − 2y = −14.

1. x − 2 y = 14
2. x − 2 y = −14
3. x + 2 y =  14
4. x + 2 y = −14

We know B is correct!

Here is how you know an answer is wrong:

D is incorrect because the points (0, 7), (2, 8) (4, 9) & (6, 10) will not satisfy the equation x + 2y = −14.

Your Turn

Which of the following equations best describes the graph shown below? Check your answer by clicking on the equation.

Interactive popup. Assistance may be required. 3x − 4y =  −12 Incorrect, solve for y, y = 3 over 4 3 4 x + 3: wrong y−intercept. Also, the points (0, −4), (3, −8) and (−3, 0) on the graph do not work in the equation 3x − 4y = −12. Interactive popup. Assistance may be required. 4x + 3y = −12 Correct! Solve for y, y = - 4 over 3 4 3 x - 4. Double check: the points (−3, 0), (0, −4), and (3, −8) on the graph work in the equation 4x + 3y = −12. Interactive popup. Assistance may be required. 4x + 3y = 4 Incorrect, solve for y, y = - 4 over 3 4 3 x + 4 over 3 4 3 : wrong y−intercept. Also, the points (−3, 0), (0, −4), and (3, −8) on the graph do not work in the equation 4x + 3y = 4. I hope this tells you what the correct answer ought to be. (Get it? ought to Be) Interactive popup. Assistance may be required. 4x − 3y = −12 Incorrect, solve for y, y = 4 over 3 4 3 x + 4: wrong y-intercept and slope. Also, the points (−3, 0), (0, −4), and (3, −8) on the graph do not work in the equation 4x − 3y = −12.