Ch 4.7 Objective: To use the slope and y-intercept to graph lines.

Definitions Slope-Intercept Form Slope (m) and y-intercept (b) written in the form: y = mx + b Parallel Lines Parallel lines have the SAME SLOPE but different y-intercepts

Rules Steps for Graphing 1) Plot the y-intercept point: (0, b) 2) Plot a second point using m = rise/run 3) Draw a line through the two points

Slope-Intercept Form of the Linear Equation Any linear equation which is solved for y is in slope-intercept form. y = mx + b Find the slope and y-intercept of the following linear equations: 1) y = 3x + 4 2) y = - 2x - 1 3) y = 5x 4) y = x ) y = x ) y = 6 m = 3 b = 4 m = - 2 b = - 1 m = 5 b = 0 m = b = m = b = m = 0 b = 6

Parallel Lines: Example 1 Are these lines parallel? y = 3x + 2 y = 3x + 5 These equations both have slope (m=3) but they have different y-intercepts [(0, 2) & (0, 5)]

Tell whether the lines below are parallel. 1) 3x + y = 7 y = -3x x y = -3x + 7 m = -3 y = mx + b m = -3 Lines are parallel! Same slope!

Example #1 Graph: y = 2x + 3 1) Plot the point (0,3) 2) m = 2 (2 units up and 1 unit over) so a second point would be (1,5) 1 3) Draw a line through the two points

Graph the line which passes through (-2, 1) and has a slope of -3. x y 1) Plot the point. Steps 2) Write slope as fraction and count up and over. m = - 3 = or m = ) Draw line through points. Example 2

Graph the line which passes through (3, 2) and has a slope of. x y 1) Plot the point. Steps 2) Write slope as fraction and count up and over. m = or m = ) Draw line through points. 3 4 Example 3

Graph the line which passes through (-5, 4) and has a slope of. x y 1) Plot the point. Steps 2) Write slope as fraction and count up and over. m = ) Draw line through points Example 4

-3-3 Graph the following linear equation using slope and y-intercept. x y 1) Find the slope and y-intercept. Steps 2) Plot the y-intercept. m = 2 3 or m = ) Draw line through points. 3) Plot the slope Example 5

Graph the following linear equation using slope and y-intercept. x y 1) Find the slope and y-intercept. Steps 2) Plot the y-intercept. m = -1 2 or m = 1 4) Draw line through points. 3) Plot the slope Example 6

Slope-Intercept Form of the Linear Equation Write a linear equation in the form y = mx + b given the following. 1) m = 2, b = -3 2) m =, b = 5 3) m =, y-int.= 2 4) m = 0, b = 6 5) m =, b = 0 6) m = 1, b = y = 2x - 3 y = 6

Write a linear equation in slope-intercept form to describe each graph. x y x y b = 3 y = 2x + 3 b = -4

Parallel Lines Graph the following on the coordinate plane. x y Parallel lines have the same slope.

Write a linear equation to describe this situation and graph. Kyle has $300 and is saving $25 a week. Let x = # of weeksLet y = savings in dollars y = 25x changestart value y = mx + b Slope Y-intercept Savings Weeks m = $25 / week b = 300

Pam received $100 and spends $4 each week. 1) Write an equation for the money, y, she has after x weeks. 2) What are the slope and y-intercept? y = x m = - 4 b = 100