Point-Slope Form 4-7 Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1 Holt McDougal Algebra 1

Objectives Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.

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) Write the 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) y – y1 = m(x – x1) Write the point-slope form. Substitute –4 for m, 0 for x1 and 3 for y1. y – 3 = –4(x – 0) y – 3 = –4(x – 0)

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) y – y1 = m(x – x1) Write the point-slope form. Substitute 1 for m, –1 for x1, and –4 for y1. y – (–4) = 1(x – (–1)) Rewrite subtraction of negative numbers as addition. y + 4 = 1(x + 1)

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) y – y1 = m(x – x1) Write the point-slope form. Substitute 0 for m, 3 for x1 and –4 for y1. y – (–4) = 0(x – 3) Rewrite subtraction of negative numbers as addition. y + 4 = 0(x – 3)

Additional Example 2A: Using Point-Slope Form to Graph Graph the line described by the equation. y – 1 = 2(x – 3) (2,5) y – 1 = 2(x – 3) is in the form y – y1= m(x – x1). (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.

Additional Example 2B: Using Point-Slope Form to Graph Graph the line described by the equation. (2,7) y – 4 = (x – (–2)) is in the form y – y1= m(x – x1). (-2,4) The line contains the point (–2, 4). slope: m = Step 1 Plot (–2, 4). Step 2 Count 3 units up and 4 units right and plot another point. Step 3 Draw the line connecting the two points.

Additional Example 2C: Using Point-Slope Form to Graph Graph the line described by the equation. y + 3 = 0(x – 4) y – (–3) = 0(x – 4) is in the form y – y1= m(x – x1). The line contains the point (4, –3). slope: m = 0 Step 1 Plot (4, –3). Step 2 There slope is 0. Every value of x will be at y = –3. Step 3 Draw the line connecting the points.

Check It Out! Example 2a Graph the line described by the equation. y + 2 = –(x – 2) y – (–2) = –1(x − 2) is in the form y – y1 = m(x – x1). The line contains the point (2, –2). Step 1 Plot (2, –2). Step 2 Count 1 unit down and 1 unit right and plot another point. Step 3 Draw the line connecting the points.

Graph the line described by the equation. Check It Out! Example 2b Graph the line described by the equation. y + 3 = –2(x – 1) y – (–3) = –2(x − 1) is in the form y – y1= m(x – x1). The line contains the point (1, –3). (0,-1) slope: m = –2 (1,-3) Step 1 Plot (1, –3). Step 2 Count 2 units up and 1 unit left and plot another point. Step 3 Draw the line connecting the points.

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

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) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point-slope form. y – y1 = m(x – x1) y – (–3) = 2(x – 2) Choose (2, –3).

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