Determine the slopes and intercepts for each segment of linear function represented in the graph. ITEM BANK: Move to Bottom slope = -1/2slope = 1slope = 1/4x-intercept (-10,0) x-intercept (-3,0) x-intercept (10,0) y-intercept (0,3) y-intercept (0,5) y-intercept (0,5/2)
orange line green line and blue line

color : {slope, x-intercept, y-intercept} = ...

  orange : {-1/2, (10, 0), (0, 5)}

  green : {1, (-3, 0), (0, 3)}

  blue: {1/4, (-10, 0), (0, 5/2)}

Step-by-step explanation:

Slope

The slope of each segment can be found by counting grid squares. The "rise" is the distance the right end is above the left end. The "run" is the horizontal distance from the left end to the right end. The slope is ...

  slope = rise/run

For the orange segment, we have a rise of -1, and a run of 2, so the slope is -1/2.

For the green segment, we have a rise of 2, and a run of 2, so the slope is 2/2 = 1.

For the blue segment, we have a rise of 1, and a run of 4, so the slope is 1/4.

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Intercepts

To find the x- and y-intercepts, it is convenient to simply extend each of the line segments until it crosses both x- and y-axes. You can do this by eye, using a straightedge, or by counting grid squares.

The orange line will cross the y-axis at 5 and the x-axis at 10. (The ratio of these numbers is 5/10, the opposite of the slope.)

The green line will cross the y-axis at 3 and the x-axis at -3. (The ratio of these numbers is 3/-3 = -1, the opposite of the slope.)

The blue line will cross the y-axis at 2.5 = 5/2, and the x-axis at -10. (The ratio of these numbers is 2.5/-10 = -1/4, the opposite of the slope.)

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A summary of slopes and intercepts is provided in the Answer block, above.

3

step-by-step explanation:

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: