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Published byNora Shaw Modified over 6 years ago

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Graphing Linear Equations

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Linear Equation An equation for which the graph is a line

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Solution Any ordered pair of numbers that makes a linear equation true. (9,0) IS ONE SOLUTION FOR Y = X - 9

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Linear Equation Example: y = x + 3

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Graphing Step 1: ~ Three Point Method ~ Choose 3 values for x

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Graphing Step 2: Find solutions using table y = x + 3 X | Y 0 1 2

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Graphing Step 3: Graph the points from the table (0,3) (1,4) (2,5)

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Graphing Step 4: Draw a line to connect them

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Try These Graph using a table (3 point method) 1) y = x + 3 2) y = x - 4

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Slope-Intercept y = mx + b m = slope b = y-intercept

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Slope-Intercept The m in the slope-intercept form is ALWAYS attached to the X variable. The slope is NEVER including the X variable For example, if given y = 3x + 4 the slope is 3 NOT 3x.

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Y-intercept Where the line crosses the y-axis

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Y-intercept The y-intercept has an x-coordinate of ZERO

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Y-intercept To find the y- intercept, plug in ZERO for x and solve

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Y-Intercept Summary The y-intercept is the b in the slope intercept form. This b (y-intercept) is your starting point on the graph. –To easily remember this, think of b as you Beginning point. For example, in y = 3x + 4 the Beginning point is at (0,4) {Remember: to find the y- intercept, plug on zero for the x.}

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X-intercept Where the line crosses the x-axis

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X-intercept The x-intercept has a y coordinate of ZERO

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X-intercept To find the x- intercept, plug in ZERO for y and solve

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Slope Describes the steepness of a line

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Slope Equal to: Rise Run

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Rise The change vertically, the change in y

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Run The change horizontally or the change in x

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Finding Slope Step 1: Find 2 points on a line (2, 3) (5, 4) (x 1, y 1 ) (x 2, y 2 )

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Finding Slope Step 2: Find the RISE between these 2 points Y 2 - Y 1 = 4 - 3 = 1

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Finding Slope Step 3: Find the RUN between these 2 points X 2 - X 1 = 5 - 2 = 3

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Finding Slope Step 4: Write the RISE over RUN as a ratio Y 2 - Y 1 = 1 X 2 - X 1 3

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Step 1: Mark a point on the y-intercept

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Step 2: Define slope as a fraction...

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Step 3: Numerator is the vertical change (RISE)

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Step 4: Denominator is the horizontal change (RUN)

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Step 5: Graph at least 3 points and connect the dots

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