Graphing Linear Equations

An equation for which the graph is a line Linear Equation An equation for which the graph is a line

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

Linear Equation Example: y = x + 3

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

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

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

Draw a line to connect them Graphing Step 4: Draw a line to connect them

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

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

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.

Where the line crosses the y-axis Y-intercept Where the line crosses the y-axis

The y-intercept has an x-coordinate of ZERO

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

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.}

Where the line crosses the x-axis X-intercept Where the line crosses the x-axis

The x-intercept has a y coordinate of ZERO

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

Describes the steepness of a line Slope Describes the steepness of a line

Slope Equal to: Rise Run

The change vertically, the change in y Rise The change vertically, the change in y

The change horizontally or the change in x Run The change horizontally or the change in x

Finding Slope Step 1: Find 2 points on a line (2, 3) (5, 4) (2, 3) (5, 4) (x1, y1) (x2, y2)

Find the RISE between these 2 points Finding Slope Step 2: Find the RISE between these 2 points Y2 - Y1 = 4 - 3 = 1

Find the RUN between these 2 points Finding Slope Step 3: Find the RUN between these 2 points X2 - X1 = 5 - 2 = 3

Write the RISE over RUN as a ratio Finding Slope Step 4: Write the RISE over RUN as a ratio Y2 - Y1 = 1 X2 - X1 3

Mark a point on the y-intercept Step 1: Mark a point on the y-intercept

Define slope as a fraction... Step 2: Define slope as a fraction...

Step 3: Numerator is the vertical change (RISE)

Denominator is the horizontal change Step 4: Denominator is the horizontal change (RUN)

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