4.2 Notes Alg1.notebook
November 15, 2012
4­2 Using Integers
Skills we've learned
Tell whether each set of ordered pairs satisfies a linear function. Explain.
1. {(–3, 10), (–1, 9), (1, 7), (3, 4), (5, 0)}
2. {(3, 4), (5, 7), (7, 10), (9, 13), (11, 16)}
Tell whether each function is linear. If so, graph the function.
4. 3y = 12
3. y = 3 – 2x
Skills we need
Warm­up Answers
4.2 Notes Alg1.notebook
November 15, 2012
4.2 Notes Alg1.notebook
November 15, 2012
4.2 Notes Alg1.notebook
November 15, 2012
4.2 Notes Alg1.notebook
November 15, 2012
4­2 Using Integers
Find x­ and y­ intercepts and interpret their
meanings in real­world situations.
Use x­ and y­ intercepts to graph lines
Using intercepts, divers can determine the time a safe ascent will take.
Definition of x­ and y­ Intercepts
The y­intercept is the y­coordinate of the point where the graph intersects the y­axis. The x­coordinate of this point is always 0. The x­intercept is the x­coordinate of the point where the graph intersects the x­axis. The y­coordinate of this point is always 0. 4.2 Notes Alg1.notebook
November 15, 2012
I. Finding the Intercepts Graphically
The graph intersects the y­axis at (__, __). The graph intersects the y­axis at (__, __). The graph intersects the y­axis at (__, __). The y­intercept is _____.
The y­intercept is _____.
The y­intercept is _____.
The graph intersects the x­axis at (__, __). The graph intersects the x­axis at (__, __). The graph intersects the x­axis at (__, __). The x­intercept is _____.
The x­intercept is _____.
The x­intercept is _____.
4.2 Notes Alg1.notebook
November 15, 2012
II. Finding Intercepts Algebraically
–3x + 5y = 30
To find the x­intercept, replace y with 0 and solve for x.
4x + 2y = 16
To find the y­intercept, replace x with 0 and solve for y.
4.2 Notes Alg1.notebook
November 15, 2012
3y ­ 8 = 2x
4x + 6y = 9x ­ 10
III. Applications of Intercepts
Trish can run the 200 m dash in 25 s. The function f(x) = 200 – 8x gives the distance remaining to be run after x seconds. Graph this function and find the intercepts. What does each intercept represent?
Neither time nor distance can be
negative, so choose several nonnegative values for x. Use
the function to generate ordered pairs.
x
0
5
10
20
25
f(x) =200 ­ 8x
x­intercept: _____
x­intercept: 25. This is the time it takes Trish to finish the race, or when the distance remaining is 0. y­intercept: _____
y­intercept: 200. This is the number of meters Trish has to run at the start of the race.
4.2 Notes Alg1.notebook
November 15, 2012
The school sells pens for $2.00 and notebooks for $3.00. The equation 2x + 3y = 60 describes the number of pens x and notebooks y that you can buy for $60. Neither pens nor notebooks can be negative, so choose several nonnegative values for x. Use the function to generate ordered pairs.
x
0
9
15
30
Graph the ordered pairs. Connect the points with a line.
y
x­intercept: _____
y­intercept: _____
What do these intercepts tell you in terms of the problem?
x­intercept: 30. This is the number of pens that can be purchased if no notebooks are purchased. y­intercept: 20. This is the number of notebooks that can be purchased if no pens are purchased.
IV. Graphing Linear Equations by Intercepts
Use intercepts to graph the line described by the equation.
3x – 7y = 21
1. Find the intercepts
2. Graph the intercepts
3. Connect the intercepts with a line
4.2 Notes Alg1.notebook
November 15, 2012
Use intercepts to graph the line described by the equation.
–3x + 4y = –12
y = –x + 4
If the equation is in standard form, it is easier to calculate the intercepts.
Use intercepts to graph the line described by the equation.
hint: clear the fraction and put into standard form
4.2 Notes Alg1.notebook
November 15, 2012
If the x­intercept is 5 and the y­intercept is 2,
this does NOT mean that the line has the point (5, 2)
4­2 p.240 #2 ­ 17 all, 21 ­ 27, 30 ­ 32, 34 ­ 37
*30 problems