Linear Functions

1. Linear Functions Lesson 3: Equation of a Line in Slope-intercept form and General form

2. Today’s Objectives • Relate linear relations expressed in: slope-intercept form, general form, and slope-point form to their graphs, including: • Express a linear relation in different forms, and compare graphs • Rewrite a linear relation in either slope-intercept or general form • Graph, with or without technology, a linear relation in slope-intercept, general, or slope-point form • Identify equivalent linear relations from a set of linear relations • Match a set of linear relations to their graphs

3. Vocabulary • Slope-intercept form • The equation of a line in the form where m is the slope and b is the y-intercept • General form • The equation of a line in the form where A, B, and C are integers

4. Equations of a Linear Function • We can make an equation that describes a line’s location on a graph. This is called a linear equation. There are three forms of linear equation that we will be looking at: • Standard Form: Ax + By + C = 0, where A, B, and C are integers. • Slope y-intercept form: y = mx + b, where m is the slope, and b is the y-intercept. • Slope-point form: y – y1 = m(x – x1), where m is the slope, and the line passes through a point located at (x1, y1) • For today, we will look at the first two forms.

5. Slope y-intercept form • When graphing lines, the slope y-intercept form is useful. This is because all the information you need to graph the line is found in the equation. • If we know the slope of the line, and the y-intercept, we can graph the line by using the following steps: • Step 1) Plotthe y-intercept • Step 2) From the y-intercept, count the rise and the run. • Step 3) Drawa line through both points.

6. Slope y-intercept form • Step 1) Plot the y-intercept • Step 2) From the y-intercept, count the rise and the run. • Step 3) Draw a line through both points. Rise=-1 Run=2

7. Writing an equation for a given graph • In certain cases, we will be asked to write the equation of a line given its graph. Look at the following example: y-intercept = -4 Find another point on the line that is easily read from the graph. Count out the rise and the run between the two points. (-2,-1) Rise= -3 Equation = Run=2

8. General form (or standard form) • Another form for the equation of a linear function is general form, or standard form: • In certain situations you will be asked to change the equation from slope y-intercept form into general form, and vice versa. • When converting the equation into standard form, we must remember that A, B, and C, MUST be integers, which means all fractions need to be removed. We also need to remember to move all terms to the same side of the equation to make it equal to zero.

9. Changing between forms • Change the equation into standard form. • Solution: • The first step is to multiply all terms by 3 in order to get rid of the denominator. • Next, we should move all terms to the one side of the equation. • Finally, we should arrange the terms into the correct order. • *If the sign of the Ax term is negative, we should always multiply the equation by -1 to make the first term positive.

10. Changing between forms • It is important to rearrange equations into the form before trying to graph the lines. • Rearrange the equation and graph the line • Solution: • First, isolate the y term on the left side of the equation • Next, divide all the terms by the coefficient on the y term

11. Changing between forms • Graph our equation in slope y-intercept form on the provided coordinate plane • Solution:

12. Your turn • Write the equation of the line that has a y-intercept of 5 and a slope of -1/4 in general form and in slope y-intercept form. • Solution: • Slope y-intercept form: • Convert to general form: • General form:

13. Homework • Pg. 362-364 #12,13,14,16,17,20 • Pg. 384-385 #6,8,11,12,15,16 • Quiz next class! (Slopes)

14. Wall Quiz!