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

Holt McDougal Algebra 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 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)

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.

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

Holt McDougal Algebra 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 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. Additional Example 2B: Using Point-Slope Form to Graph

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

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

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) 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 Additional Example 3C: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form.

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

Holt McDougal Algebra 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 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 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 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)y − 9 = –(x − 0) 2. Slope = ; (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 4. (0, 4) and (–7, 2) are on the line y = –2x + 5 y = x + 4