Question

find the x - and y - intercepts of each linear function. describe what the intercepts mean.

1. descent of eagle
2. evas distance from home

time (min) x\tdistance (mi) y
0\t4
2\t3
4\t2
6\t1
8\t0
graph each equation by using the x - and y - intercepts.

1. y = 4 + 2x
2. 5 - y = - 3x
3. x = 5y + 5
4. x + y = 4
5. x - y = - 3
6. y = 8 - 6x

Explanation:

21. For "Descent of Eagle"

Step1: Find x - intercept

Set \(y = 0\). Looking at the graph, when \(y=0\) (height is 0), the line intersects the \(x\) - axis at \(x = 7\). The \(x\) - intercept is the time when the eagle reaches the ground.

Step2: Find y - intercept

Set \(x = 0\). When \(x = 0\), \(y=20\). The \(y\) - intercept represents the initial height of the eagle.

Step1: Find the slope \(m\)

\(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 4}{8 - 0}=-\frac{1}{2}\)

Step2: Find the \(y\) - intercept

The \(y\) - intercept is the value of \(y\) when \(x = 0\). From the table, when \(x = 0\), \(y = 4\).

Step3: Find the \(x\) - intercept

Set \(y = 0\) in the equation \(y=4-\frac{1}{2}x\). Then \(0 = 4-\frac{1}{2}x\), so \(\frac{1}{2}x=4\) and \(x = 8\). The \(x\) - intercept means the time when Eva reaches home, and the \(y\) - intercept means her initial distance from home.

Step1: Find \(x\) - intercept

Set \(y = 0\). Then \(0=4 + 2x\), so \(2x=-4\) and \(x=-2\)

Step2: Find \(y\) - intercept

Set \(x = 0\). Then \(y=4\)

Answer:

\(x\) - intercept: 7 (time when eagle reaches ground); \(y\) - intercept: 20 (initial height of eagle)

22. For "Eva's Distance from Home"

First, find the equation of the line using the two - point form \(y - y_1=\frac{y_2 - y_1}{x_2 - x_1}(x - x_1)\). Let \((x_1,y_1)=(0,4)\) and \((x_2,y_2)=(8,0)\)