Graphing Linear Equations

Identifying a Linear Equation

A linear equation is any equation that can be put in the form...

Ax + By = C

... where A, B, and C are real numbers, and A and B are not both zero.

The graph of a linear equation is a line.

Which of the following equations are linear equations?

3x + y = 8 2(x + 3)(x + 4) = y

2x2 + 3x + 4 = y 5y + x = 1

–3x2 – y = 9 8x – 3x + x – 4 = y

The Graph of a Linear Equation

One way to graph a linear equation:

• Make a table of at least three ordered pairs

• Plot the points (x, y) on a coordinate grid.• Connect the points with a straight line.

Complete the table of values for y = 3x + 1, then graph the ordered pairs on a coordinate grid.

x y

–2

0

2

that make the equation true.

The Graph of a Linear Equation

One way to graph a linear equation:

• Make a table of at least three ordered pairs

• Plot the points (x, y) on a coordinate grid.• Connect the points with a straight line.

Complete the table of values for y = 3x + 1, then graph the ordered pairs on a coordinate grid.

x y

–2 –5

0 1

2 7

that make the equation true.

The Slope of a Linear Equation

To find the slope, m, of a graphed line, you need:

• any two points on the line: (x , y ) and (x , y )

• to write and simplify the following ratio:

2 21 1

What is the slope of 3x + y = 8?

m =

(y2 – y1)

(x2 – x1)

rise

run=

The Slope of a Linear Equation

To find the slope, m, of a graphed line, you need:

• any two points on the line: (x , y ) and (x , y )

• to write and simplify the following ratio:

2 21 1

What is the slope of 3x + y = 8?

m = –3

m =

(y2 – y1)

(x2 – x1)

rise

run=

Forms of a Linear Equation

Slope-Intercept Form:

y = mx + b, where m is the slope and b is the y-intercept

Point-Slope Form:

y – y = m(x – x ), where m is the slope and

Write y – 1 = 3x in Slope-Intercept form.

1 1

1 1

Find the slope and the y-intercept.

Use the Point-Slope form to write the equation for the line that passes through points (1, 3) and (–11, –5) in Ax + By

= C form.

x and y are the coordinates for any point on the line

Forms of a Linear Equation

Slope-Intercept Form:

y = mx + b, where m is the slope and b is the y-intercept

Point-Slope Form:

y – y = m(x – x ), where m is the slope and

Write y – 1 = 3x in Slope-Intercept form.

1 1

1 1

Find the slope and the y-intercept.

Use the Point-Slope form to write the equation for the line that passes through points (1, 3) and (–11, –5) in Ax + By

= C form.

y = 3x + 1; m = 3; y-intercept is 1

2x – 3y = –7

x and y are the coordinates for any point on the line

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