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Graphing Linear Equations Using Slope and Intercepts Objectives: …to write an equation in slope-intercept form ...to graph a linear equation using slope and the y-intercept ...to find the x-intercept and y-intercept of a linear equation ...to graph a linear equation using intercepts Assessment Anchor: 8.C.3.1 – Plot and/or identify ordered pairs on a coordinate plane. 8.D.4.1 – Represent relationships with tables or graphs on the coordinate plane. Vocabulary alert!! Y-INTERCEPT (of a line) – the point where the line intersects the y-axis NOTES y = mx + b “m” is the slope (slope-intercept form) “b” is the y-coordinate of the y-intercept To graph linear equations (using slope-intercept form): 1. Rearrange the equation so that it is in slope-intercept form 2. Determine the y-intercept and plot that point on the graph. 3. Determine the slope and use it to plot a second point. a. Make the slope a fraction if it’s not already. b. Beginning at the y-intercept…use the “rise” number to travel up or down, use the “run” number to travel left or right. 4. Connect the two points with a straight line and use arrows. Graphing Linear Equations Using Slope and Intercepts EXAMPLES 1) y = -3x – 2 y = mx + b y = -3x – 2 (already in form) y-intercept (0, -2) slope m= 2) 3y = 2x + 6 y-intercept ( , ) slope m= 3) 3x + 2y = -8 y-intercept ( , slope m= ) Graphing Linear Equations Using Slope and Intercepts Vocabulary alert!! X-INTERCEPT (of a line) – the point where the line intersects the x-axis MORE NOTES and EXAMPLES To find an X-intercept: To find a Y-intercept: A. Replace the “y” with zero B. Solve the equation for “x” A. Replace the “x” with zero B. Solve the equation for “y” 4) 3y – 2x = 12 Find the x-intercept Find the y-intercept 3(0) – 2x = 12 -2x = 12 -2 -2 x = -6 3y – 2(0) = 12 3y = 12 3 3 y=4 x-intercept: (-6, 0) y-intercept: (0, 4) 5) 2x + 4y = -2 Find the x-intercept Find the y-intercept 2x + 4(0) = -2 2x = -2 2 2 x = -1 2(0) + 4y = -2 4y = -2 4 4 y = -½ x-intercept: (-1, 0) y-intercept: (0, -½) Graphing Linear Equations Using Slope and Intercepts 6) Find the x-intercept Find the y-intercept 7) Find the x-intercept 3x – 4y = -6 10y = -2x + 15 Find the y-intercept “This now means…that there are THREE methods we can use to graph linear equations. We can use a T-table, or we can use slope-intercept form, or we can find the intercepts!”