Equations of Linesand

Graphing Them

Equations of Lines• Vertical line x = #• Horizontal line y = #• Slope, y-intercept y=mx+b • Standard Form Ax+By = C using

intercepts • Standard Form using magic

COORDINATE PLANE

Parts of a plane1. X-axis2. Y-axis3. Origin4. Quadrants I-IV

X-axis

Y-axis

Origin ( 0 , 0 )

QUAD IQUAD II

QUAD III QUAD IV

Slope-Intercept form of a line

SLOPE ReviewSlope is the ratio of the vertical rise to the horizontal run between any two points on a line. Usually referred to as the rise over run. Slope triangle between two

points. Notice that the slope triangle can be drawn two different ways.

Rise is -10 because we went down

Run is -6 because we went to the left

3

5

6

10

iscasethisinslopeThe

Rise is 10 because we went up

Run is 6 because we went to the right

3

5

6

10iscasethisinslopeThe

SLOPE-INTERCEPT FORM OF A LINEThe slope intercept form of a line is y = mx + b“m” represents the slope “b” represents the y-intercept.

♥When an equation is in slope-intercept form the

“y” is always on one side by itself.

♥If a line is not in slope-intercept form, then we must solve for “y” to get it there.

Write the equation of the line with a y-intercept of 3

and a slope of 2 Then…. graph it.

y = 2x + 3

First stepSecond step

Third step – draw the line

IN SLOPE-INTERCEPT NOT IN SLOPE-INTERCEPT

y = 3x – 5 y – x = 10

y = -2x + 10 2y – 8 = 6x

y = -.5x – 2 y + 4 = 2x

Put y – x = 10 into slope-intercept form

Add x to both sides and would get y = x + 10

Put 2y – 8 = 6x into slope-intercept form.

Add 8 to both sides then divide by 2 and would get y = 3x + 4

Put y + 4 = 2x into slope-intercept form.

Subtract 4 from both sides and would get y = 2x – 4.

Using Intercepts to Graph

The x-intercept is point where graph touches (or crosses) the x-axis.

The y-intercept is point where graph touches (or crosses) the y-axis.

1. To find x-intercepts, let y be zero and solve the equation for x.

2. To find y-intercepts, let x be zero and solve the equation for y.

Finding Interceptsof an Equation

X AND Y INTERCEPTSThe x-intercept is the x-coordinate of a point where the graph crosses the x-axis.

The y-intercept is the y-coordinate of a point where the graph crosses the y-axis.

The x-intercept would be 4 and is located at the point (4, 0).

The y-intercept is 3 and is located at the point (0, 3).

The Intercepts

Y-Intercept = 6

X-Intercept = 2

The intercepts are where

the line crosses the

axis.

Finding the intercepts•3x + y = 6 To find the x-intercept,

let y = 0•3x + (0) = 6•3x = 6

Finding the intercepts•3x + y = 6 To find the y-intercept,

let x = 0•3(0) + y = 6

The graph of 3x + y = 6

x-intercept = 2y-intercept = 6

Finding the interceptsx + 5y = 10

find the x-interceptx + 5(0) = 10x = 10 find the y-intercept

0 + 5y = 105y = 10y = 2

The coordinates are (10, 0) and (0, 2)

The graph of x + 5y = 10

x-intercept = 10y-intercept = 2

1. Find your x-intercept: Let y = 0-2x + 3(0) = 12x = -6; (-6, 0)

2. Find your y-intercept:Let x = 0-2(0) + 3y = 12y = 4; (0, 4)

3. Graph both points and draw a line through them.

Graphing with intercepts:-2x + 3y = 12

Find the intercepts and graph3x + 4y = 12

x = 4y = 3Coordinates are: (4, 0) and (0, 3)

The graph of 3x + 4y = 12

x-intercept = 4y-intercept = 3

Find the intercepts and graph

y = 4x - 4move the 4x-4x + y = -4GO!

x = 1y = -4

Oh, no! What now?

Writing and Graphingusing

Standard Form of a line

Write the equation in Standard Form:Ax + By = C

y = 2x + 3Get your variables on one side of the equation and the constant on the other.

-2x + y = 3

You’re not done…. the coefficient of x must be a positive integer.

2x – y = -3

Write the equation in Standard Form:Ax + By = C

y = 2/5x - 3Get your variables on one side of the equation and the constant on the other.

-2/5x + y = -3

Check the coefficient of x. Guess we’re not done yet.Multiply the equation by -52x – 5y = 15

Write the equation in Standard Form:Ax + By = C

y = 2/5x - 3OR….You recognize that the coefficient of x needs work: Multiply the equation by 5.

5y = 2x - 3

Move the variables to one side:-2x + 5y = -15Multiply by -12x – 5y = 15

Graphing a line from Standard Form Using Magic

Slope = -A B

x - intercept =C A

y - intercept =C B

Ax + By = C

2x – y = -3

For example:

Slope = -A B

x - intercept =C A

y - intercept =C B

Slope = -2 = 2

-1x - intercept =-3 2

y - intercept =-3 = 3 -1

Knowing this can set up your equation to graph in EITHER slope-intercept form or graphing by intercepts!!

Here’s your cheat sheet!♥ If the equation is in STANDARD FORM

(Ax + By = C), graph using the intercepts or your magic formulas.

♥ If the equation is in SLOPE-INTERCEPT FORM (y = mx + b), graph using slope and intercept or a t-table (whichever is easier for you).

♥ If the equation is in NEITHER form, rewrite the equation in the form you like the best!