linear functions identify and graph linear equations name and graph x and y intercepts
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Linear FunctionsLinear FunctionsIdentify and Graph Linear EquationsIdentify and Graph Linear Equations
Name and Graph X and Y InterceptsName and Graph X and Y Intercepts
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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.
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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.
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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.
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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)
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x-intercept (7, 0)
y-intercept (0, -2)
Now, draw a line through the points.
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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)
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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
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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)
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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.
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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.
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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.
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ExerciseExercise
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ChallengeChallenge