Point Slope Form

Table of Contents 26: Warm-Up, Guided Practice 27: How Do I Write an Equation With a Slope and Point?

Warm - Up Identify the slope and y-intercept of the following linear functions: 1. f(x) = 3x – 1 2. r(x) = 2 – x 3. y(x) = ½x 4. x -1 1 2 h(x) -4 -7

Learning Intention/Success Criteria LI: We are learning to write equations using a point and a slope SC: I know how to -solve simple linear equations -compute the symbolic form of a linear function given its slope and point -given a slope and point in context, construct the symbolic form of a linear function -find the point-slope form of a linear equation

EQ: How Do I Write an Equation With a Slope and Point? 11/27/2018

A number which is used to indicate the steepness of a line and if the line is tilted uphill or downhill Slope Indicated by the letter “m” Point The pair of numbers giving the location on a coordinate plane. Written in the form: (x, y)

The point at which the function crosses the y-axis Y-Intercept Slope Intercept Form A way of writing an equation with a slope and a y-intercept Written: f(x) = mx + b, where m is the slope and b is the y-intercept.

A way of writing an equation with a point and a slope. Point – Slope Form Written: y – y1 = m(x – x1) where m is the slope and (x1, y1) is the point.

y = mx + b Example 1: Use slope-intercept form to write a linear equation m = 3 f(-1) = 2 m: x: y: 3 -1 2 2 = (3)(-1) + b 2 = -3 + b +3 +3 _________ 5 = b y = 3x + 5

Guided Practice 1 Use slope-intercept form to write a linear equation. f(x) has a slope of -4 and f(-1) = 3

Guided Practice 1 Use slope-intercept form to write a linear equation. f(x) has a slope of -4 and f(-1) = 3 A] f(x) = -4x – 1 B] f(x) = -4x + 3 C] f(x) = -4x + 1 D] f(x) = -4x – 3

Guided Practice 1 Use slope-intercept form to write a linear equation. f(x) has a slope of -4 and f(-1) = 3 y = mx + b f(x) = -4x - 1 3 = (-4)(-1) + b 3 = 4 + b -4 -4 _________ -1 = b

Guided Practice 2 Use slope-intercept form to write a linear equation. g(x) has a slope of ½ and goes through (2, 3)

Guided Practice 2 Use slope-intercept form to write a linear equation. g(x) has a slope of ½ and goes through (2, 3) A] g(x) = 1/2x + 2 B] g(x) = 1/2x + 3 C] g(x) = 1/2x + 1/2 D] g(x) = 1/2x + 0

Guided Practice 2 Use slope-intercept form to write a linear equation. g(x) has a slope of ½ and goes through (2, 3) y = mx + b f(x) = 1/2 x + 2 3 = ( ½ )(2) + b 3 = 1 + b -1 -1 _________ 2 = b

y – y1 = m(x – x1) Example 2: Use point-slope form to write a linear equation m = 3 pt: (1, 5) m: x: y: 3 1 5 y – 5 = 3(x – 1)

Guided Practice 3 Use point-slope form to write a linear equation. h(x) has a slope of 2/3 and goes through (0, -1)

Guided Practice 3 Use point-slope form to write a linear equation. h(x) has a slope of 2/3 and goes through (0, -1) A] y = 2/3x – 1 B] y = 2/3x C] y + 1 = 2/3x D] y – 1 = 2/3x + 0

Guided Practice 3 Use point-slope form to write a linear equation. h(x) has a slope of 2/3 and goes through (0, -1) y – y1 = m(x – x1) y – -1 = 2/3(x – 0) y + 1 = 2/3(x – 0) y + 1 = 2/3(x)

Guided Practice 4 Use point-slope form to write a linear equation. m = 4 and f(3) = -5

Guided Practice 4 Use point-slope form to write a linear equation. m = 4 and f(3) = -5 A] y + 5 = 4(x – 3) B] y – 5 = 4(x – 3) C] y + 5 = 4(x + 3) D] y – 5 = 4(x + 3)

Guided Practice 4 Use point-slope form to write a linear equation. m = 4 and f(3) = -5 y – y1 = m(x – x1) y – -5 = 4(x – 3) y + 5 = 4(x – 3)

Example 3: Go from point – slope form to slope – intercept form y – 4 = ½ (x + 10) y – 4 = ½x + 5 + 4 + 4 ________________ y = ½x + 9

Guided Practice 5 Go from point - slope form to slope - intercept form y – 8 = -1/4 (x + 4)

Guided Practice 5 Go from point - slope form to slope - intercept form y – 8 = -1/4 (x + 4) A] y = -1/4x + 8 B] y = -1/4x + 4 C] y = -1/4x + 9 D] y = -1/4x + 7

Guided Practice 5 Go from point - slope form to slope - intercept form y – 8 = -1/4 (x + 4) y – 8 = -1/4x – 1 + 8 + 8 _________________ y = -1/4x + 7