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Slope intercept
 

Slope intercept

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    Slope intercept Slope intercept Presentation Transcript

    • Practice converting linear equations into Slope-Intercept Form It’s easier than you think…
    • Slope intercept form is: y = mx + b Our main goal is to get the y alone on one side of the equation
    • Convert Into Slope-Intercept Form (divide both sides by 2 to get y alone) (now simplify all fractions) 2 1
    • When an equation is in slope-intercept form: y = mx + b 2 What is the slope? ____________ What is the intercept? ____________ 1 slope Now look at the equation below…… Intercept
    • y = 2x + 1 Step 1: Look at the y-intercept and plot where the graphs cross the “y” axis. Now look at the graph of the line. Step 2: Use the slope (rise/run) to determine the next point and plot. Step 3: Draw a line through both points. Be sure to extend pass point and put arrow at both ends.
    • *** Easy *** 5y = 10x + 15 Convert to Slope-Intercept Form: (divide both sides by 5 to get y alone) (now simplify all fractions) y = 2x + 3
    • y = 2x + 3
    • *** Now Try this Convert to Slope-Intercept Form *** -3y = -9x - 12 Step 1: divide both sides by -3 to get y alone Step 2: Simplify all fractions Step 3: Write your equation in y = mx + b What is the slope? ____________ What is the intercept? ____________
    • *** Check Your Answer *** -3y = -9x - 12 (divide both sides by -3 to get y alone) (now simplify all fractions) y = 3x + 4 Slope = 3 Intercept = 4 -3 -3 -3y = -9x - 12 -3 -3 -3
    • y = 3x + 4 Slope = 3 Intercept = 4 Because there is no room to move up 3 we will have to move down 3 and to the LEFT 1
    • *** medium *** 21x – 7y =14 Convert to Slope-Intercept Form: (subtract both sides by 21x) -7y = -21x + 14 (now divide both sides by -7) y = 3x – 2 (simplify all fractions)
    • 2y + 26 = -6x Step 1: Subtract both sides by 26 Step 2: Divide both sides by 2 to get y by itself Step 3: Simplify all fractions *** Now Try this Convert to Slope-Intercept Form *** What is the slope? ____________ What is the intercept? ____________
    • 2y + 26 = -6x (subtract both sides by 26) 2y = -6x - 26 (now divide both sides by 2 y = -3x - 13 (simplify all fractions) *** Check Your Answer ***
    • Vocabulary The word “intercept” means to cross.
    • Vocabulary x-intercept - the point (ordered pair) where a line crosses the x-axis. y-intercept - the point (ordered pair) where a line crosses the y-axis.
    • Intercepts Find the x and y intercepts of the line below. x y -3 -2 -1 1 2 3 3 2 1 -1 -2 -3
    • Intercepts Find the x and y intercepts of the line below. x y Where does the line cross the x-axis? x-intercept is (-2,0) -3 -2 -1 1 2 3 3 2 1 -1 -2 -3
    • Intercepts Find the x and y intercepts of the line below. x Where does the line cross the y-axis? x-intercept is (-2,0) y-intercept is (0,2) Sometimes, this is written as x-intercept = -2 and y-intercept = 2. y -3 -2 -1 1 2 3 3 2 1 -1 -2 -3
    • Intercepts Find the x and y intercepts of the line below. x y -3 -2 -1 1 2 3 3 2 1 -1 -2 -3
    • Intercepts Find the x and y intercepts of the line below. x Where does the line cross the x-axis? x-intercept is (1,0) y -3 -2 -1 1 2 3 3 2 1 -1 -2 -3
    • Intercepts Find the x and y intercepts of the line below. x Where does the line cross the y-axis? x-intercept is (1,0) y-intercept is (0,3) y -3 -2 -1 1 2 3 3 2 1 -1 -2 -3
    • Intercepts Find the x and y intercepts of the line below. x y -3 -2 -1 1 2 3 3 2 1 -1 -2 -3
    • Intercepts Find the x and y intercepts of the line below. x Where does the line cross the x-axis? x-intercept is (-1,0) y 3 2 1 -1 -2 -3 -3 -2 -1 1 2 3
    • Intercepts Find the x and y intercepts of the line below. x Where does the line cross the y-axis? x-intercept is (-1,0) y-intercept is (0,½ ) y -3 -2 -1 1 2 3 3 2 1 -1 -2 -3
    • Intercepts Sometimes, we must find the intercepts without a graph. x y -3 -2 -1 1 2 3 3 2 1 -1 -2 -3
    • Intercepts Sometimes, we must find the intercepts without a graph. We use the equation of the line.
    • Intercepts To find the x intercept, let y = 0 To find the y intercept, let x = 0 Substitute 0 for y. Substitute 0 for x.
    • Intercepts Find the x and y intercepts of the graph of the equation 2x – 5y = 10. x-intercept y-intercept The x-intercept is (5,0). The y-intercept is (0,–2).