Point-Slope Form & Graphing Lesson 36

Objectives HSF-LE.2: Construct linear functions given a graph, description of a relationship, or two input-output pairs.

Point-Slope Form of an Equation Because the slope of line is constant, it is possible to use any point on a line and the slope of the line to write an equation of the line in point-slope form. Recall 1) 𝑥 1 , 𝑦 1 is a point on the graph 2) m = slope

Example; Find an equation of the line Write the equation of the line in point-slope form and in slope-intercept form with slope –5 through (1, 3). Point-Slope Form Slope-Intercept form. y – 3 = –5(x – 1) y – y1 = m(x – x1) y – 3 = –5x + 5 y – (3) = –5(x – 1) Substitute. Distribute. y = –5x + 8 Solve for y. y – 3 = –5(x – 1) Simplify. y - 3= -5(x – 1) y = -5x + 8

Example; Find an equation of the line Write the equation of the line in slope-intercept form through (–2, –3) and (2, 5). Use points: (-2, -3) and (2, 5) m = 𝒚 𝟏 − 𝒚 𝟐 𝒙 𝟏 − 𝒙 𝟐 = 𝟓−−𝟑 𝟐−−𝟐 = 𝟖 𝟒 = 𝟐 Point-Slope Form Slope-Intercept form. y – 5 = 2(x - 2) y – y1 = m(x – x1) y – 5 = 2x - 4 Distribute. y – (5) = 2(x – 2) Substitute. y = 2x + 1 Solve for y. y – 5 = 2(x – 2) Simplify. y - 5= 2(x – 2) y = 2x + 1

Example; Graph the line 𝑦− 4 =− 2 3 𝑥− −3 y 1 𝑥 1 Slope m = − 2 3 Point = (-3, 4)

Example; Graph the line 𝑦− −1 = 1 3 𝑥− 3 y 1 𝑥 1 Slope m = 1 3 Point = (3, -1)

#36: Point-Slope Form & Graphing Questions? Summarize Notes Homework Google Classroom Quiz