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5-8 Point-Slope Form Objectives Graph a line and write a linear equation using point-slope form. Write a linear equation given two points. Holt McDougal Algebra 1 5-8 Point-Slope Form If you know the slope and any point on the line, you can write an equation of the line by using the slope formula. For example, suppose a line has a slope of 3 and contains (2, 1) . Let (x, y) be any other point on the line. Substitute into the slope formula. Multiply both sides by (x - 2). Simplify. Holt McDougal Algebra 1 5-8 Point-Slope Form Holt McDougal Algebra 1 5-8 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. y – y1 = m (x – x1) Holt McDougal Algebra 1 Write the point-slope form. 5-8 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) Holt McDougal Algebra 1 5-8 Point-Slope Form 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. slope = 1; (–1, –4) Holt McDougal Algebra 1 5-8 Point-Slope Form Check It Out! Example 1b Write an equation in point slope form for the line with the given slope that contains the given point. slope = 0; (3, –4) Holt McDougal Algebra 1 5-8 Point-Slope Form In Lesson 5-7, you graphed a line given its equation in slope-intercept form. You can also graph a line when given its equation in point-slope form. Start by using the equation to identify a point on the line. Then use the slope of the line to identify a second point. Holt McDougal Algebra 1 5-8 Point-Slope Form Additional Example 2A: Using Point-Slope Form to Graph Graph the line described by the equation. y – 1 = 2(x – 3) y – 1 = 2(x – 3) is in the form y – y1= m(x – x1). (2,5) (1,3) The line contains the point (3, 1). Step 1 Plot (3, 1). Step 2 Count 2 units up and 1 unit right and plot another point. Step 3 Draw the line connecting the two points. Holt McDougal Algebra 1 5-8 Point-Slope Form Additional Example 2B: Using Point-Slope Form to Graph Graph the line described by the equation. Holt McDougal Algebra 1 5-8 Point-Slope Form Additional Example 2C: Using Point-Slope Form to Graph Graph the line described by the equation. y + 3 = 0(x – 4) Holt McDougal Algebra 1 5-8 Point-Slope Form Check It Out! Example 2a Graph the line described by the equation. y + 2 = –(x – 2) Holt McDougal Algebra 1 5-8 Point-Slope Form Additional Example 3A: Writing Linear Equations in Slope-Intercept Form Write the equation that describes each line in slope-intercept form. Slope = 3, (–1, 4) is on the line. Step 1 Write the equation in point-slope form: y – y1 = m(x – x1) y – 4 = 3[x – (–1)] Step 2 Write the equation in slope-intercept form by solving for y. Rewrite subtraction of negative numbers as addition. y – 4 = 3(x + 1) Distribute 3 on the right side. y – 4 = 3x + 3 +4 +4 Add 4 to both sides. y = 3x + 7 Holt McDougal Algebra 1 5-8 Point-Slope Form Additional Example 3B: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. (2, –3) and (4, 1) Holt McDougal Algebra 1 5-8 Point-Slope Form Additional Example 3C: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. Holt McDougal Algebra 1 5-8 Point-Slope Form Check It Out! Example 3a Write the equation that describes the line in slope-intercept form. Holt McDougal Algebra 1 5-8 Point-Slope Form Check It Out! Example 3b Write an equation in slope-intercept form for the line through the two points. (1, –2) and (3, 10) Holt McDougal Algebra 1 5-8 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). Holt McDougal Algebra 1 5-8 Point-Slope Form Check It Out! Example 4 Write an equation in slope-intercept form for the line through the two points. (2, 15) and (–4, –3) Holt McDougal Algebra 1 5-8 Point-Slope Form Lesson Quiz Write an equation in slope-intercept form for the line with the given slope that contains the given point. 1. Slope = –1; (0, 9) 2. Slope = y − 9 = –(x − 0) ; (3, –6) y + 6 = (x – 3) Write an equation that describes each line the slope-intercept form. 3. Slope = –2, (2, 1) is on the line y = –2x + 5 4. (0, 4) and (–7, 2) are on the line y = Holt McDougal Algebra 1 x+4