Standard form of a linear equation is Ax + By = C, where A, B, and C are integers and Ax and By are on the same side of the equation. To find the x-intercept and y-intercept, set y = 0 and x = 0 respectively and solve for the remaining variable. The intercepts can then be used to graph the line. Given a point and slope, the slope-intercept form can be found and then converted to the standard form Ax + By = C. If two points are given, the slope is found first before converting to standard form.

1. Standard Form Ax + By = C Section 5.7

2. Standard form in General Standard form is tricky Some textbooks will give you Ax + By = C Others will give you Ax + By + C = 0 Others may give you some slightly different variation Focus on the A, B, C for Standard Form.

3. Ax + By = C A, B, C must be integers A, B, C can NOT be decimals or fractions Ax & By must be on the same side of the equation It is preferred that A be positive (not necessary, but preferred) That means that 4x - 3y = 6 is the same thing as -4x + 3y = -6

4. Example 1- Find x & y intercepts of equations To find the x-intercept, replace y with 0 & solve for x. To find the y-intercept, replace x with 0 & solve for y. This works because: x-intercept is (x, 0) y-intercept is (0,y)

5. Example 1- Find x & y intercepts of equations You can use the x & y intercepts to graph. Just plot the two intercepts and draw the line through the two points.

6. Example 2 - Graph equations in standard form Use inverse operations to move the equation into slope intercept form. Change of instructions above problem 17 on the back: Rewrite the equation to slope-intercept form

7. Example 3 - Word Problems We are going to do Example 4 before we do Example 3. We’ll come back to Example 3.

8. Example 4 - Find Standard Form from a point and the slope You will be given a point & the slope We found slope-intercept form from a point and the slope in lesson 5-5.

9. Example 4 - Find Standard Form from a point and the slope After you find slope intercept form: Multiply the equation by an LCD to get rid of any denominators. Use inverse operations to move any terms one at a time until the equation is in Ax + By = C form.

10. One Last Thing If you are given two points and told to put it in Standard Form: Find the slope Use the slope and one of the points to find slope-intercept form. Then follow the instructions on the previous screen to move the equation into standard form.

11. Review What is Standard Form. How do you find the x & y intercepts? How do you use the intercepts to graph an equation? How do you graph an equation from standard form?

12. Review What steps do you take to solve a word problem? What steps do you take to write a standard form equation given a point and the slope? What steps do you take to write a standard form equation given two points?