5 8 PointSlope Form Objectives Graph a line

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 Mc. Dougal 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 Mc. Dougal Algebra 1

5 -8 Point-Slope Form Holt Mc. Dougal Algebra 1

5 -8 Point-Slope Form Additional Example 1 A: 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 – y 1 = m (x – x 1) Holt Mc. Dougal Algebra 1 Write the point-slope form.

5 -8 Point-Slope Form Additional Example 1 B: 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 Mc. Dougal Algebra 1

5 -8 Point-Slope Form Additional Example 1 C: 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 Mc. Dougal Algebra 1

5 -8 Point-Slope Form Check It Out! Example 1 b Write an equation in point slope form for the line with the given slope that contains the given point. slope = 0; (3, – 4) Holt Mc. Dougal 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 Mc. Dougal Algebra 1

5 -8 Point-Slope Form Additional Example 2 A: Using Point-Slope Form to Graph the line described by the equation. y – 1 = 2(x – 3) is in the (1, 3) form y – y 1= m(x – x 1). 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 Mc. Dougal Algebra 1 (2, 5)

5 -8 Point-Slope Form Additional Example 2 B: Using Point-Slope Form to Graph the line described by the equation. Holt Mc. Dougal Algebra 1

5 -8 Point-Slope Form Additional Example 2 C: Using Point-Slope Form to Graph the line described by the equation. y + 3 = 0(x – 4) Holt Mc. Dougal Algebra 1

5 -8 Point-Slope Form Check It Out! Example 2 a Graph the line described by the equation. y + 2 = –(x – 2) Holt Mc. Dougal Algebra 1

5 -8 Point-Slope Form Additional Example 3 A: 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 – y 1 = m(x – x 1) 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 = 3 x + 3 +4 +4 Add 4 to both sides. y = 3 x + 7 Holt Mc. Dougal Algebra 1

5 -8 Point-Slope Form Additional Example 3 B: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. (2, – 3) and (4, 1) Holt Mc. Dougal Algebra 1

5 -8 Point-Slope Form Additional Example 3 C: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. Holt Mc. Dougal Algebra 1

5 -8 Point-Slope Form Check It Out! Example 3 a Write the equation that describes the line in slope-intercept form. Holt Mc. Dougal Algebra 1

5 -8 Point-Slope Form Check It Out! Example 3 b Write an equation in slope-intercept form for the line through the two points. (1, – 2) and (3, 10) Holt Mc. Dougal 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 Mc. Dougal 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 Mc. Dougal 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 = – 2 x + 5 4. (0, 4) and (– 7, 2) are on the line y = Holt Mc. Dougal Algebra 1 x+4