warm up 0?1? 2? graph the linear functions.0?1? 2?
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Warm Warm UpUp
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22 ??
Graph the linear functions.
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11 ??
22 ??
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INTERCEPTS OF GRAPHSINTERCEPTS OF GRAPHS
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ObjectivesObjectives
Graph and interpret linear Functions. (AF 3.0)Graph and interpret linear Functions. (AF 3.0)
Represent quantitative relationships Represent quantitative relationships graphically and interpret the meaning of a graphically and interpret the meaning of a specific part of the graph in the situation specific part of the graph in the situation represented by the graph. (AF 1.5) represented by the graph. (AF 1.5)
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INTERCEPTS OF A INTERCEPTS OF A GRAPHGRAPH
InterceptsIntercepts- - points at which the graph intersects points at which the graph intersects the the xx-- or or yy--axis.axis.
What number do the x- and y- intercepts What number do the x- and y- intercepts have in common?have in common?
Finding intercepts:Finding intercepts: An An xx-intercept is written as the ordered pair (-intercept is written as the ordered pair (xx, ,
0).0). A A yy-intercept is written as the ordered pair (0, -intercept is written as the ordered pair (0, yy).).
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The graph of any The graph of any linear linear equation in two variables equation in two variables is a is a straight linestraight line..
y
x
Intercepts
• Finding intercepts can be helpful when graphing.
• The x-intercept is the point where the line crosses the x-axis.
• The y-intercept is the point where the line crosses the y-axis.
x - intercept
y - intercept
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Finding the Finding the interceptsintercepts
1)1) To find the x - interceptTo find the x - intercept of a line, substitute of a line, substitute y = 0 into the equation and solve for x.y = 0 into the equation and solve for x.
2) To find the y - intercept2) To find the y - intercept of a line, substitute of a line, substitute x = 0 into the equation and solve for y.x = 0 into the equation and solve for y.
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Finding the x - interceptFinding the x - intercept Find the x-intercept of the graph of the equation y =2x-6Find the x-intercept of the graph of the equation y =2x-6
To find the x-intercept: To find the x-intercept:
substitute in ZERO for y and solve for y.substitute in ZERO for y and solve for y.
y = 2x-6 write the equationy = 2x-6 write the equation
0=2x -6 substitute 0 for y 0=2x -6 substitute 0 for y
+6 +6 +6 +6 solve for xsolve for x
6=2x6=2x
3=x 3=x
Thus, the x-intercept is (3,0).Thus, the x-intercept is (3,0).
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Finding the y - interceptFinding the y - intercept
Find the y-intercept of the graph of the equation y =2x-6Find the y-intercept of the graph of the equation y =2x-6
To find the y-intercept: To find the y-intercept:
substitute in ZERO for x and solve for y.substitute in ZERO for x and solve for y.
y = 2x-6 write the equationy = 2x-6 write the equation
y = 2(y = 2(00) -6 substitute 0 for x ) -6 substitute 0 for x
y = 0-6y = 0-6 solve for ysolve for y
y = -6y = -6
Thus, the y- intercept is (0,-6).Thus, the y- intercept is (0,-6).
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Find the intercepts of y = Find the intercepts of y = 4x+44x+4
To find the x - intercept: To find the x - intercept:
Let y = 0 Let y = 0
y = 4x+4y = 4x+4
0=4x +40=4x +4
-4 -4 -4 -4
solve for xsolve for x -4=4x-4=4x
-1 = x -1 = x Thus, the x-intercept is Thus, the x-intercept is
(-1,0).(-1,0).
To find the y - To find the y - intercept: intercept:
let x=0let x=0 y = 4x+4 y = 4x+4
y = y = 4(4(00) +4) +4 y = 0+4y = 0+4
solve for ysolve for y y = 4y = 4
Thus, the y -intercept Thus, the y -intercept is (0,4). is (0,4).
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You tryYou try Find the intercepts of the graph of y = -Find the intercepts of the graph of y = -
3x+63x+6 To find the x - intercept: To find the x - intercept:
Let y = 0 Let y = 0
y = -3x+6y = -3x+6
0=-3x +60=-3x +6
-6 -6 -6 -6
solve for xsolve for x -6=-3x-6=-3x
2= x 2= x Thus, the x-intercept is Thus, the x-intercept is
(2,0).(2,0).
To find the y - To find the y - intercept: intercept:
let x=0let x=0 y = -3x+6 y = -3x+6
y y = -3(= -3(00) +6) +6 y = 0+6y = 0+6
solve for ysolve for y y = 6y = 6
Thus, the y -intercept Thus, the y -intercept is (0,6). is (0,6).
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Identify the Identify the interceptsintercepts
1) x - intercept:1) x - intercept:
y - intercept:y - intercept:
2) x - intercept:2) x - intercept:
y - intercept:y - intercept:
3) x - intercept:3) x - intercept:
y - intercept:y - intercept:4
2
2
-1
-2
-2
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Sketch a graph using the Sketch a graph using the interceptsintercepts
x - intercept: 4 x - intercept: 4
y - intercept: 3
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Sketch a graph using the Sketch a graph using the interceptsintercepts
1) x - intercept: -21) x - intercept: -2
y - intercept: 3y - intercept: 3
2) x - intercept: 22) x - intercept: 2
y - intercept: 4y - intercept: 4
3) x - intercept:-33) x - intercept:-3
y - intercept:-4y - intercept:-4