Holt McDougal Algebra Slope-Intercept Form Warm Up Find each y-intercept. 1. y = 3x x – 3y = 12 Find each slope x + 2y = x + 2 = 6y Solve each equation for y. 4. 6x + 2y = 6 2 –4 –3 y = –2x + 5

Holt McDougal Algebra Slope-Intercept Form Write a linear equation in slope-intercept form. Graph a line using slope-intercept form. Objectives Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.

Holt McDougal Algebra Slope-Intercept Form Additional Example 1: Graphing by Using Slope and y-intercept Graph the line given the slope and y-intercept. Step 1 The y-intercept is 4, so the line contains (0, 4). Plot (0, 4). Step 3 Draw the line through the two points. Run = 5 Rise = –2 Step 2 Slope = Count 2 units down and 5 units right from (0, 4) and plot another point. y ; y intercept = 4 Slope =-

Holt McDougal Algebra Slope-Intercept Form Any linear equation can be written in slope-intercept form by solving for y and simplifying. In this form, you can immediately see the slope and y-intercept. Also, you can quickly graph a line when the equation is written in slope-intercept form.

Holt McDougal Algebra Slope-Intercept Form Additional Example 2A: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. slope = ; y-intercept = 4 y = mx + b y = x + 4 Substitute the given values for m and b. Simply if necessary.

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

Holt McDougal Algebra Slope-Intercept Form Additional Example 2C: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. Step 1 Find the y-intercept. The graph crosses the y-axis at (0, 3), so b = 3. Step 2 Find the slope. The line contains the points (–4, 1) and (–2, 2).

Holt McDougal Algebra Slope-Intercept Form Additional Example 2C Continued Write the equation that describes the line in slope-intercept form. Use the slope formula. Substitute (–4,1) for (x 1, y 1 ) and (–2, 2) for (x 2, y 2 ). y = mx + b Write the slope-intercept form. Step 3 Write the equation.

Holt McDougal Algebra Slope-Intercept Form slope = 2; (3, 4) is on the line. y = mx + b Substitute 2 for m, 3 for x, and 4 for y. 4 = 2(3) + b Step 1 Find the y-intercept. –2 = b 4 = 6 + b –6 Write the slope-intercept form. Solve for b. Since 6 is added to b, subtract 6 from both sides to undo the addition. Additional Example 2D: Writing linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form.

Holt McDougal Algebra Slope-Intercept Form Additional Example 2D Continued Step 2 Write the equation. y = mx + b Write the slope-intercept form. Substitute 2 for m, and –2 for b. y = 2x + (–2) y = 2x – 2 slope = 2; (3, 4) is on the line. Write the equation that describes the line in slope-intercept form.

Holt McDougal Algebra Slope-Intercept Form Additional 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.

Holt McDougal Algebra Slope-Intercept Form Additional Example 3B: Using Slope-Intercept Form to Graph Write the equation in slope-intercept form. Then graph the line described by the equation. 2y + 3x = 6 Step 1 Write the equation in slope-intercept form by solving for y. 2y + 3x = 6 –3x –3x 2y = –3x + 6 Subtract 3x from both sides. Since y is multiplied by 2, divide both sides by 2.

Holt McDougal Algebra Slope-Intercept Form Additional Example 3B Continued Step 2 Graph the line. slope: m = y-intercept: b = 3 Plot (0, 3). Count 3 units down and 2 units right and plot another point. Draw the line connecting the two points. Write the equation in slope-intercept form. Then graph the line described by the equation. is in the form y = mx + b.

Holt McDougal Algebra Point-Slope Form

Holt McDougal Algebra Point-Slope Form Additional Example 1A: Writing Linear Equations in Point-Slope Form Write an equation in point slope form for the line with the given slope that contains the given point. Write the point-slope form. y – y 1 = m (x – x 1 )

Holt McDougal Algebra Point-Slope Form Additional Example 1B: Writing Linear Equations in Point-Slope Form Write an equation in point slope form for the line with the given slope that contains the given point. slope = –4; (0, 3) Write the point-slope form. y – y 1 = m(x – x 1 ) y – 3 = –4(x – 0) Substitute –4 for m, 0 for x 1 and 3 for y 1. y – 3 = –4(x – 0)

Holt McDougal Algebra Point-Slope Form slope = 1; (–1, –4) Additional Example 1C: Writing Linear Equations in Point-Slope Form Write an equation in point slope form for the line with the given slope that contains the given point. Write the point-slope form. y – (–4) = 1(x – (–1)) Substitute 1 for m, –1 for x 1, and –4 for y 1. y + 4 = 1(x + 1) Rewrite subtraction of negative numbers as addition. y – y 1 = m(x – x 1 )

Holt McDougal Algebra Point-Slope Form Additional Example 2A: Using Point-Slope Form to Graph y – 1 = 2(x – 3) Graph the line described by the equation. y – 1 = 2(x – 3) is in the form y – y 1 = m(x – x 1 ). The line contains the point (3, 1). Step 2 Count 2 units up and 1 unit right and plot another point. Step 1 Plot (3, 1). Step 3 Draw the line connecting the two points. (1,3) (2,5)

Holt McDougal Algebra Point-Slope Form Graph the line described by the equation. The line contains the point (–2, 4). Step 2 Count 3 units up and 4 units right and plot another point. Step 1 Plot (–2, 4). (-2,4) (2,7) Step 3 Draw the line connecting the two points. Additional Example 2B: Using Point-Slope Form to Graph y – 4 = (x – (–2)) is in the form y – y 1 = m(x – x 1 ). slope: m =

Holt McDougal Algebra Point-Slope Form Graph the line described by the equation. y + 3 = 0(x – 4) y – (–3) = 0(x – 4) is in the form y – y 1 = m(x – x 1 ). The line contains the point (4, –3). Step 2 There slope is 0. Every value of x will be at y = –3. Step 1 Plot (4, –3). slope: m = 0 Step 3 Draw the line connecting the points. Additional Example 2C: Using Point-Slope Form to Graph

Holt McDougal Algebra Point-Slope Form Write the equation that describes each line in slope-intercept form. Additional Example 3A: Writing Linear Equations in Slope-Intercept Form Slope = 3, (–1, 4) is on the line. Step 1 Write the equation in point-slope form: y – 4 = 3[x – (–1)] Step 2 Write the equation in slope-intercept form by solving for y. y – 4 = 3(x + 1) Rewrite subtraction of negative numbers as addition. Distribute 3 on the right side. y – 4 = 3x y = 3x + 7 Add 4 to both sides. y – y 1 = m(x – x 1 )

Holt McDougal Algebra Point-Slope Form (2, –3) and (4, 1) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point-slope form. Choose (2, –3). y – y 1 = m(x – x 1 ) y – (–3) = 2(x – 2) Additional Example 3B: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form.

Holt McDougal Algebra Point-Slope Form Step 3 Write the equation in slope-intercept form. y = 2x – 7 –3 Additional Example 3B Continued Write an equation in slope-intercept form for the line through the two points. (2, –3) and (4, 1) y + 3 = 2(x – 2) y + 3 = 2x – 4

Holt McDougal Algebra Point-Slope Form Additional Example 3C: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. Step 2 Find the slope.

Holt McDougal Algebra Point-Slope Form Additional Example 3C Continued Write the equation that describes the line in slope-intercept form. Step 3 Write the equation in slope-intercept form. y = mx + b y = –4x + 1 Write the slope-intercept form. Substitute –4 for m and 1 for b.

Holt McDougal Algebra Point-Slope Form Additional Example 4: Using Two Points Find Intercepts Write an equation in slope-intercept form for the line through (10, –3) and (5, –2). Step 1 Find the slope. Step 2 Write the equation in slope-intercept form. Write the point-slope form. Subtract 3 from both sides.

Holt McDougal Algebra Point-Slope Form Step 3 Find the intercepts. x-intercept: Replace y with 0 and solve for x. The x-intercept is –5, and the y-intercept is –1. Additional Example 4 Continued y-intercept: Use the slope- intercept form to indentify the y- intercept.

Holt McDougal Algebra Point-Slope Form Homework Section 4-6 and 4-7 in the workbook Workbook page 223: 1 – 7 Workbook page 229: 1, 2, and 3