Graphing Linear Equations

Linear Equation

An equation for which the graph is

a line

SolutionAny 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

GraphingStep 2:

Find solutions using tabley = x + 3X | Y 0 1 2

Graphing

Step 3:

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

Graphing

Step 4:

Draw a line to connect them

Try These

• Graph using a table (3 point method)

1) y = x + 3

2) y = x - 4

Slope-Intercept

y = mx + bm = 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.

Y-intercept

Where the line crosses the

y-axis

Y-intercept

The y-intercept has an x-coordinate of

ZERO

Y-intercept

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.}

X-intercept

Where the line crosses the

x-axis

X-intercept

The x-intercept has a y coordinate of

ZERO

X-intercept

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

solve

Slope

Describes the steepness of a

line

Slope

Equal to:

Rise Run

Rise

The change vertically, the change in y

Run

The change horizontally or

the change in x

Finding SlopeStep 1:

Find 2 points on a line

(2, 3) (5, 4)

(x1, y1) (x2, y2)

Finding SlopeStep 2:

Find the RISE between these 2

points

Y2 - Y1 =

4 - 3 = 1

Finding SlopeStep 3:

Find the RUN between these 2

points

X2 - X1 =

5 - 2 = 3

Finding SlopeStep 4:

Write the RISE over RUN as a ratio

Y2 - Y1 = 1

X2 - X1 3

Step 1:

Mark a point on the y-intercept

Step 2:

Define slope as a fraction...

Step 3: Numerator is the vertical change

(RISE)

Step 4:

Denominator is the horizontal

change

(RUN)

Step 5:

Graph at least 3 points and

connect the dots