Point-Slope Form Section 5-4 Part 1

Goals Goal Rubric To write and graph linear equations using point-slope form. Level 1 – Know the goals. Level 2 – Fully understand the goals. Level 3 – Use the goals to solve simple problems. Level 4 – Use the goals to solve more advanced problems. Level 5 – Adapts and applies the goals to different and more complex problems.

Vocabulary Point-Slope Form of a Line

Substitute into the slope formula. 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. Slope formula Multiply both sides by (x – 2). 3(x – 2) = y – 1 Simplify. y – 1 = 3(x – 2)

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.

Point-Slope Form y – y1 = m(x – x1) slope y-coordinate x-coordinate (x1, y1) represents a specific point and (x, y) represents any point. y – y1 = m(x – x1) slope y-coordinate x-coordinate

Example: 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. A. B. C.

Your Turn: Write an equation in point-slope form for the line with the given slope that contains the given point. a. b. slope = 0; (3, –4) y – (–4) = 0(x – 3) y + 4 = 0(x – 3)

Example: Writing Linear Equations Using Point-Slope Form Write an equation in slope-intercept form for the line with slope 3 that contains (–1, 4). Step 1 Write the equation in point-slope form: y – y1 = m(x – x1) y – 4 = 3[x – (–1)] Step 2 Rewrite the equation in slope-intercept form by solving for y. Rewrite subtraction of negative numbers as addition. y – 4 = 3(x + 1) y – 4 = 3x + 3 Distribute 3 on the right side. + 4 + 4 Add 4 to both sides. y = 3x + 7

Your Turn: Write an equation in slope-intercept form for the line with slope that contains (–3, 1). Step 1 Write the equation in point-slope form: y – y1 = m(x – x1)

Continued Step 2 Rewrite the equation in slope-intercept form by solving for y. Rewrite subtraction of negative numbers as addition. Distribute on the right side. +1 +1 Add 1 to both sides.

Point-Slope Form and Graphing In Lesson 5-3, you saw that if you know the slope of a line and the y-intercept, you can graph the line. You can also graph a line if you know its slope and any point on the line.

Example: Graphing Using Point-Slope form Graph the equation What is the ordered pair? (x1, y1) = What is the slope? m = (2, 5) (2, 5)

Your Turn: Graph the equation What is the ordered pair? (x1, y1) = What is the slope? m = (-2, 5)

Example: Graphing Given a Point and the Slope Graph the line with the given slope that contains the given point. slope = 2; (3, 1) Step 1 Plot (3, 1). 1 • Step 2 Use the slope to move from (3, 1) to another point. 2 • (3, 1) Move 2 units up and 1 unit right and plot another point. Step 3 Draw the line connecting the two points.

Example: Graphing Given a Point and the Slope Graph the line with the given slope that contains the given point. slope = ; (–2, 4) (2, 7) 4 • Step 1 Plot (–2, 4). 3 (–2, 4) • Step 2 Use the slope to move from (–2, 4) to another point. Move 3 units up and 4 units right and plot another point. Step 3 Draw the line connecting the two points.

Example: Graphing Given a Point and the Slope Graph the line with the given slope that contains the given point. slope = 0; (4, –3) A line with a slope of 0 is horizontal. Draw the horizontal line through (4, –3). • (4, –3)

Your Turn: Graph the line with slope –1 that contains (2, –2). Step 1 Plot (2, –2). Step 2 Use the slope to move from (2, –2) to another point. (2, –2) • −1 • Move 1 unit down and 1 unit right and plot another point. 1 Step 3 Draw the line connecting the two points.

Joke Time Why do milking stools only have three legs? Because the cow’s got the udder! What did the mother Buffalo say when her boy left for college? Bye-Son! What do you do with a sick boat? Take it to the doc.

Assignment 5-4 Part 1 Exercises Pg. 340: #6 – 18 even