Linear FunctionsLinear FunctionsIdentify and Graph Linear EquationsIdentify and Graph Linear Equations

Name and Graph X and Y InterceptsName and Graph X and Y Intercepts

Vocabulary for this Vocabulary for this lessonlesson

Linear Equation – the equation of Linear Equation – the equation of a line whose graph is a straight a line whose graph is a straight line.line.

Standard Form – Linear equations Standard Form – Linear equations written in the form Ax + By + C= 0written in the form Ax + By + C= 0

X-Intercept – the point where a X-Intercept – the point where a graphed line crosses the x-axis.graphed line crosses the x-axis.

Y-Intercept – the point where a Y-Intercept – the point where a graphed line crosses the y-axis.graphed line crosses the y-axis.

Determine whether each Determine whether each equation is linear….if so, write equation is linear….if so, write it in Standard Formit in Standard Form

Can it be written Can it be written in standard form? in standard form? Ax + By = C Ax + By = C

1) y = 5 – 2x+2x +2x2x + y = 5

2) y = -3 – x + x + x x + y = -3

3) 2xy – 5y = 6 Why?....The first term has TWO variables.

4) 1/3 y = -1

Can it be written Can it be written in standard form? in standard form? Ax + By = C Ax + By = C

(3) (3)

y = -3

5) 5x + 3y = z + 2

Why?....It has an extra variable “z”.

6) y = x2 – 8

Why?....Because the “x” is squared.

To be considered LINEAR, an equation must have a degree of ONE.

x and y - Interceptsx and y - Intercepts

7) 2 7 14x y To find the x-intercept, let y = 0

To find the y-intercept, let x = 0

2 7(0) 14x 2 0 14x

2 14x 2 2

7x

2(0) 7 14y 0 7 14y

7 14y 7 7

2y The x-int. is 7, so the graph intersects the x-axis at (7, 0)

The y-int. is -2, so the graph intersects the y-axis at (0, -2)

x-intercept (7, 0)

y-intercept (0, -2)

Now, draw a line through the points.

Find the x & y intercepts, Find the x & y intercepts, then graph the equation.then graph the equation.

8) x + y = -58) x + y = -5

x + 0 = -5x + 0 = -5x = -5x = -5

(-5, (-5, 0)0)

0 + y = -0 + y = -55y = -5y = -5

(0, -(0, -5)5)

Find the x & y intercepts, Find the x & y intercepts, then graph the equation.then graph the equation.

9) 3x + 2y = 99) 3x + 2y = 9

3x + 0 = 93x + 0 = 93x = 93x = 9

(3, 0)(3, 0)

0 + 2y = 0 + 2y = 992y = 92y = 9

(0, 4.5)(0, 4.5)

x = 3x = 3

y = 4.5y = 4.5

Determine the x & y intercepts of Determine the x & y intercepts of each linear function.each linear function.

10)xx yy

-3-3 -1-1

-2-2 00

-1-1 11

00 22

11 33

11)

x-int = -2

Or (-2, 0)

y-int = 2

Or (0, 2)

Real World ExamplesReal World ExamplesIncreasing Temperature

-5

-4

-3

-2-1

0

1

2

3

0 10 20 30 40

Time (min)

Tem

per

atu

re (

F)

Series1

x-int. of 20 means x-int. of 20 means that after 20 that after 20 minutes, the minutes, the temperature was temperature was 00°F°F..

y-int. of -4 means y-int. of -4 means that at 0 time (the that at 0 time (the beginning) the beginning) the temperature was temperature was -4 -4°F°F12) Determine the x & y intercepts

and describe what the intercepts mean.

Real World ExamplesReal World Examples13)13) Determine the x & y intercepts and describe Determine the x & y intercepts and describe

what they mean.what they mean.

Taxi Fare

-4

-2

0

2

4

6

8

-10 -5 0 5 10

Miles

Co

st (

$)

The x-int. doesn’t make sense here because it is negative.

The y-int. represents the base fare, or cost at zero miles.

Determine the Intercepts Determine the Intercepts and explain each.and explain each.

14) Draining a pool 14) Draining a pool

15) Position of a 15) Position of a scuba diver.scuba diver.Time Time

(h)(h)Volume Volume

(g)(g)

00 10,0810,0800

22 86408640

44 72007200

66 57605760

88 43204320

1010 28802880

1414 00

Time Time (s)(s)

Depth Depth (m)(m)

00 -24-24

33 -18-18

66 -12-12

99 -6-6

1212 00

The x-int. shows that after 14 hours, the pool had 0 gallons, or it was completely drained. The y-int. shows that at 0 hours, when they began, it had 10,080 gallons in it.

The x-int. shows that after 12 sec., the diver was at the surface (0 m). The y-int. shows that when he started (0 s) he was at -24m or 24m below sea level.

ExerciseExercise

ChallengeChallenge