Writing Equations From Two Points

Table of Contents 26: Warm-Up, Guided Practice 27: How Do I Write an Equation From Two Points?

Warm - Up Write an equation in slope-intercept form and point-slope form with the given information: 1. M = -6; (3, -2) 2. M = 0; (-7, 1)

Learning Intention/Success Criteria LI: We are learning to write the linear equations using two points SC: I know how to -identify slope and y-intercept -use the slope formula to find slope -write linear equations in two ways

EQ: How Do I Write an Equation With Two Points? 5/14/2019

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 Represented by the letter b Slope Intercept Form f(x) = mx + b Slope Formula m = y2 – y1 x2 – x1 Point Slope Form y – y1 = m(x – x1)

Example 1: Find the equation of the line in slope intercept form that passes through (3, 1) and (-4, 15) m = y2 – y1 x2 – x1 m = 15 – 1 -4 – 3 m = 14 -7 m = -2 y = mx + b 1 = (3)(-2) + b 1 = -6 + b + 6 + 6 ______________ 7 = b y = -2x + 7

Guided Practice 1 Using slope-intercept form, find the equation of the line that passes through (2, -5) and (8, 13) y = 3x - 11 Follow Up: What is f(-2) for this function? f(-2) = -17

Guided Practice 2 Using slope-intercept form, find the equation of the line that passes through (4, -1) and (-2, 29) y = -5x + 19 Follow Up: What is the value of x when f(x) = 9? f(x) = 9 when x = 2.

Example 2: Find the equation of the line in point slope form that passes through (-2, -7) and (1, -1) m = y2 – y1 x2 – x1 m = -1 - - 7 1 - - 2 m = 6 3 m = 2 y – y1 = m(x – x1) y - - 1 = 2(x – 1) y + 1 = 2(x – 1)

Guided Practice 3 Find the equation of the line in point slope form that passes through (80, 198) and (150, 408) y – 198 = 3(x – 80) Follow Up: What is the equivalent equation in slope intercept form? y = 3x - 42