Warm-Up Exercises Evaluate the expression for, 0, and 2. 1 = x – 1. 2x2x3 + x – 2. 3.In 2005, Carey’s Pet Shop had a profit of $55,000. In 2006, the profit was $38,700. In a graph of the data, is the slope between 2005 and 2006 positive or negative? ANSWER 1, 3, 7 ANSWER 3 5 – 1,1,, – 3 1 ANSWER negative

Example 1 Use Slope-Intercept Form to Graph a Line Graph – 2.2. = 4 3 yx SOLUTION STEP 1 Write the equation in slope- intercept form by adding to each side: 4 3 x 2.2. = 4 3 yx + STEP 2 Find the y -intercept. Comparing to, you can see that b 2. Plot a point at 2 = 4 3 yx + b = ymxmx + = ( ).). 0, 2

Example 1 Use Slope-Intercept Form to Graph a Line Find the slope. The slope is, so. From, move up 3 units and right 4 units. Plot a Second point at. STEP 4 Draw a line through the two points. STEP 3 = 4 3 m = run rise 4 3 () 4, 5 () 0, 2

Checkpoint Graph the equation. 1. = 2 1 yx ANSWER Use Slope-Intercept Form to Graph a Line

Checkpoint Graph the equation yx – = – ANSWER Use Slope-Intercept Form to Graph a Line

Checkpoint Graph the equation. 3. = 3 2 yx – 3 ANSWER Use Slope-Intercept Form to Graph a Line

Example 2 Draw Quick Graphs Graph. 3x3x+2y2y = 12 SOLUTION Method 1 Use Standard Form STEP 1 The equation is already written in standard form. x = 4 Solve for x. STEP 2 Find the x -intercept. 3x3x+ = 12 ( 02 ) Let. y = 0 The x -intercept is 4, so plot the point (4, 0).

Example 2 Draw Quick Graphs y = 6 Solve for y. 2y2y+ = 12 ( 03 ) Let. x = 0 The y -intercept is 6, so plot the point (0, 6). STEP 4 Draw a line through the intercepts. STEP 3 Find the y -intercept.

Example 2 Draw Quick Graphs 2y2y+ = 12 3x3x Standard form 2y2y+ = 12 3x3x Solve for y. – y = Slope-intercept form +6 –x 2 3 Now graph using the method of Example 1. Solve for y to rewrite the equation Method 2 Use Slope-Intercept Form

Checkpoint Graph the equation. Choose either method. 4. x+y = 7 5. y+ = 3 – x 2 1 ANSWER Draw Quick Graphs

Checkpoint Graph the equation. Choose either method. 6. 5x5x+2y2y = 10 ANSWER Draw Quick Graphs

Example 3 Graph Parallel and Perpendicular Lines Draw the graph of a. y 4 3x3x= + b. Graph the line that passes through and is parallel to the graph of () 0, 1 – y x3x= + c. Graph the line that is perpendicular to the graph of at its y -intercept. y 4 3x3x= + SOLUTION a. Draw the graph of using the y -intercept 4 and slope 3. y 4 3x3x= +.

Example 3 Graph Parallel and Perpendicular Lines b. Graph the point Any line parallel to the graph of has the same slope, 3. From move up 3 units and right 1 unit. Plot a second point at. Draw a line through the two points. ( ).). 0, 1 – ( ),), – () 1, 2 y 4 3x3x= + c. The slope of any line perpendicular to the graph of is the negative reciprocal of 3, or. So, from move down 1 unit and right 3 units. Plot a second point at. Draw the line. y 4 3x3x= + () 0, 4 () 3, –

Checkpoint Graph the line. On the same grid, graph (a) the line passing through the origin that is parallel to the original line, and (b) the line perpendicular to the original line at its y -intercept. y 12x2x = – 7. ANSWER Graph Parallel and Perpendicular Lines

Checkpoint Graph the line. On the same grid, graph (a) the line passing through the origin that is parallel to the original line, and (b) the line perpendicular to the original line at its y -intercept. 4 3 y2x = + 8. ANSWER Graph Parallel and Perpendicular Lines

Checkpoint ANSWER Graph Parallel and Perpendicular Lines Graph the line. On the same grid, graph (a) the line passing through the origin that is parallel to the original line, and (b) the line perpendicular to the original line at its y -intercept. 9. y 5 1 1x+ – =