Point-Slope Form Section 5-4 Part 1

Goals Goal To write and graph linear equations using point-slope form. Rubric 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

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

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 – y 1 = m(x – x 1 ) x-coordinatey-coordinate slope (x 1, y 1 ) represents a specific point and (x, y) represents any point.

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

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 – 4 = 3[x – (–1)] Step 2 Rewrite 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 ) Example: Writing Linear Equations Using Point-Slope Form

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 – y 1 = m(x – x 1 ) Your Turn:

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

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. Point-Slope Form and Graphing

Example: Graphing Using Point-Slope form Graph the equation What is the ordered pair? (x 1, y 1 ) = What is the slope? m = (2, 5)

Your Turn: Graph the equation What is the ordered pair? (x 1, y 1 ) = What is the slope? m = (-2, 5)

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

slope = ; (–2, 4) Step 1 Plot (–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. (–2, 4) 3 4 (2, 7) Graph the line with the given slope that contains the given point. 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) Example: Graphing Given a Point and the Slope

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. Move 1 unit down and 1 unit right and plot another point. Step 3 Draw the line connecting the two points. −1 1 (2, –2) Your Turn:

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