Remember! If you are absent, do the following BEFORE you come back to class Go to my website (type Muehleck into Google) Click on the lesson notes link on the day you were absent and go through the examples Try the homework problems listed on the day you were absent Now you won’t be behind!

Lesson Objectives: I will be able to … Graph a line and write a linear equation using point-slope form Write a linear equation given two points Language Objective: I will be able to … Read, write, and listen about vocabulary, key concepts, and examples

Graph the line given the slope and y-intercept. Check It Out! Example 1a Graph the line given the slope and y-intercept. slope = 2, y-intercept = –3 Step 1 The y-intercept is –3, so the line contains (0, –3). Plot (0, –3). Run = 1 Rise = 2 • Step 2 Slope = Count 2 units up and 1 unit right from (0, –3) and plot another point. • Step 3 Draw the line through the two points.

Example 1B: Graphing by Using Slope and y-intercept Graph the line given the slope and y-intercept. Run = 1 slope = 4; y-intercept = Rise = 4 • Step 1 The y-intercept is , so the line contains (0, ). Plot (0, ). • Step 2 Slope = Count 4 units up and 1 unit right from (0, ) and plot another point. Step 3 Draw the line through the two points.

Example 2D: Writing linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. slope = ; y-intercept = –6 y = mx + b Substitute the given values for m and b. Simply if necessary.

Example 2B: Writing linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. slope = –9; y-intercept = y = mx + b Substitute the given values for m and b. y = –9x + Simply if necessary.

Check It Out! Example 2 A line has a slope of 8 and (3, –1) is on the line. Write the equation that describes this line in slope-intercept form. Step 1 Find the y-intercept. y = mx + b Write the slope-intercept form. –1 = 8(3) + b Substitute 8 for m, 3 for x, and –1 for y. –25 = b –1 = 24 + b –24 –24 Solve for b. Since 24 is added to b, subtract 24 from both sides to undo the addition.

Check It Out! Example 2 Continued A line has a slope of 8 and (3, –1) is on the line. Write the equation that describes this line in slope-intercept form. Step 2 Write the equation. y = mx + b Write the slope-intercept form. y = 8x + (–25) Substitute 8 for m, and –25 for b. y = 8x – 25

Example 3A: Using Slope-Intercept Form to Graph Write the equation in slope-intercept form. Then graph the line described by the equation. y = 3x – 1 y = 3x – 1 is in the form y = mx + b slope: m = 3 = y-intercept: b = –1 • Step 1 Plot (0, –1). • Step 2 Count 3 units up and 1 unit right and plot another point. Step 3 Draw the line connecting the two points.

Check It Out! Example 3b Write the equation in slope-intercept form. Then graph the line described by the equation. 6x + 2y = 10 Step 1 Write the equation in slope intercept form by solving for y. 6x + 2y = 10 –6x –6x 2y = –6x + 10 Subtract 6x from both sides. Since y is multiplied by 2, divide both sides by 2.

Check It Out! Example 3b Continued Write the equation in slope-intercept form. Then graph the line described by the equation. Step 2 Graph the line. • y = –3x + 5 is in the form y = mx + b. • slope: m = y-intercept: b = 5 • Plot (0, 5). • Count 3 units down and 1 unit right and plot another point. • Draw the line connecting the two points.

Example 1: Using Slope and a Point to Graph Page 25 Graph the line with slope = 2 that contains the point (3, 1). Step 1 Plot (3, 1). Step 2 Use the slope to move from (3, 1) to another point. 1 • 2 • (3, 1) Move 2 units up and 1 unit right and plot another point. Step 3 Draw the line connecting the two points.

Graph the line with slope –1 that contains (2, –2). Your Turn 1 Page 25 Graph the line with slope –1 that contains (2, –2). Step 1 Plot (2, –2). Step 2 Use the slope to move from (2, –2) to another point. (2, –2) Move 1 unit down and 1 unit right and plot another point. • −1 • 1 Step 3 Draw the line connecting the two points.

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Example 2: Writing Linear Equations in Point-Slope Form Page 26 Write an equation in point-slope form for the line with the given slope that contains the given point. A. B. C.

Your Turn 2 Page 26 Write an equation in point-slope form for the line with the given slope that contains the given point. A. B. slope = 0; (3, –4) y – (–4) = 0(x – 3) y + 4 = 0(x – 3)

Example 3: Writing Linear Equations in Slope-Intercept Form Page 27 Write an equation in slope-intercept form for the line with slope 3 that contains (–1, 4). Step 1 Write the equation in point-slope form: y – y1 = m(x – x1) y – 4 = 3[x – (–1)] y – 4 = 3(x + 1) Step 2 Write the equation in slope-intercept form by solving for y. y – 4 = 3(x + 1) Distribute 3 on the right side. y – 4 = 3x + 3 + 4 + 4 y = 3x + 7

Step 1 Write the equation in point-slope form: Your Turn 3 Page 27 Write an equation in slope-intercept form for the line with slope that contains (–3, 1). Step 1 Write the equation in point-slope form: Step 2 Write the equation in slope-intercept form by solving for y. y – y1 = m(x – x1)

Example 4: Using Two Points to Write an Equation Page 28 Write an equation in slope-intercept form for the line through points (2, -3) and (4, 1). Step 1 Find the slope. Step 3 Write the equation in slope-intercept form. y + 3 = 2(x – 2) Step 2 Substitute the slope and one of the points into the point-slope form. y + 3 = 2x – 4 –3 –3 y = 2x – 7 y – y1 = m(x – x1) y – (–3) = 2(x – 2)

Classwork Assignment #25 Holt 5-7 #20, 21, 23, 24, 28, 29, 30, 36, 37