Question

identify the slope and y - intercept of the following equations:

1. $y = \frac{7}{3}x-17$

slope: $\frac{7}{3}$
y - intercept: - 17

1. $y=-\frac{2}{5}x + 10$

slope: $-\frac{2}{5}$
y - intercept: 10

1. $y = \frac{1}{5}x$

slope: $\frac{1}{5}$
y - intercept: 0
circle which of the following equations is an example of:

1. point - slope form

a) $y - y_1=m(x - x_2)$
b) $ax + by = c$
c) $y=mx + b$

1. slope - intercept form

a) $ax + by = c$
b) $y - y_1=m(x - x_2)$
c) $y=mx + b$

1. standard form

a) $y=mx + b$
b) $y - y_1=m(x - x_2)$
c) $ax + by = c$
interpret the slope using context from the graph
7)
gasoline tank
fuel (gallons)
distance (miles)
miles per gallon
8)
typing speed
words typed
time (minutes)
words typed per minute

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: For $y=\frac{7}{3}x - 17$

Comparing with $y = mx + b$, we get slope $m=\frac{7}{3}$ and y - intercept $b=-17$.

Step3: For $y =-\frac{2}{5}x + 10$

Comparing with $y = mx + b$, we get slope $m =-\frac{2}{5}$ and y - intercept $b = 10$.

Step4: For $y=\frac{1}{5}x$

We can rewrite it as $y=\frac{1}{5}x+0$. So slope $m=\frac{1}{5}$ and y - intercept $b = 0$.

Step5: Recall forms of linear equations

The point - slope form is $y - y_1=m(x - x_1)$; the slope - intercept form is $y=mx + b$; the standard form is $Ax + By=C$.

Step6: Answer for point - slope form

The point - slope form equation is A. $y - y_1=m(x - x_1)$.

Step7: Answer for slope - intercept form

The slope - intercept form equation is C. $y=mx + b$.

Step8: Answer for standard form

The standard form equation is C. $Ax + By=C$.

Step9: Interpret slope for gasoline tank graph

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using points $(0,9)$ and $(90,0)$ (from the graph), $m=\frac{0 - 9}{90-0}=-\frac{1}{10}$. It represents the number of gallons of fuel used per mile. The negative sign indicates the fuel is decreasing as the distance increases.

Step10: Interpret slope for typing speed graph

Using points $(1,55)$ and $(3,165)$, $m=\frac{165 - 55}{3 - 1}=\frac{110}{2}=55$. It represents the number of words typed per minute.

Answer:

1. Slope: $\frac{7}{3}$, y - intercept: $-17$
2. Slope: $-\frac{2}{5}$, y - intercept: $10$
3. Slope: $\frac{1}{5}$, y - intercept: $0$
4. A. $y - y_1=m(x - x_1)$
5. C. $y=mx + b$
6. C. $Ax + By=C$
7. The fuel in the tank decreases by $\frac{1}{10}$ gallon per mile.
8. The typing speed is 55 words per minute.