Question

a helicopter takes off from the top of a building. the helicopter’s height over time is shown in the graph.

graph: helicopter height over time, x-axis: time (min) from 0 to 8, y-axis: height (ft) from 10 to 110. points at (0, 50) and (5, 100), line connecting them.

what are the slope and the y-intercept of the function displayed in the graph?

select slope, y-intercept, or neither for each value.

value	slope	y-intercept	neither
5	○	○	○
10	○	○	○
50	○	○	○
100	○	○	○

Explanation:

Step1: Recall slope and y-intercept definitions

The slope \( m \) of a line through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). The y - intercept is the value of \( y \) when \( x = 0 \), i.e., the point \((0,b)\) where \( b \) is the y - intercept.

For the given graph, we have two points \((0,50)\) and \((5,100)\).

Step2: Calculate the slope

Using the slope formula with \((x_1,y_1)=(0,50)\) and \((x_2,y_2)=(5,100)\), we get \( m=\frac{100 - 50}{5 - 0}=\frac{50}{5}=10 \).

Step3: Analyze each value

• Value 0:
• If we consider \( x = 0 \), the y - intercept occurs at \( x = 0 \). The y - intercept is 50 (from the point \((0,50)\)), but 0 is the \( x \) - value at the y - intercept. Wait, no. Wait, the y - intercept is the \( y \) - value when \( x = 0 \). But 0 here: Let's think about the roles. The slope is 10, y - intercept is 50.
• For \( x = 0 \), it's the \( x \) - coordinate of the y - intercept point, but the y - intercept is the \( y \) - value (50) when \( x = 0 \). Wait, no, the question is about classifying the values (0,5,10,50,100) as slope, y - intercept, or neither.
• Slope is 10, y - intercept is 50.
• Value 0: Neither (since slope is 10, y - intercept is 50)
• Value 5: It's the \( x \) - coordinate of the point \((5,100)\), neither slope (10) nor y - intercept (50)
• Value 10: Slope is 10, so 10 is the slope.
• Value 50: The y - intercept is 50 (from the point \((0,50)\)), so 50 is the y - intercept.
• Value 100: It's the \( y \) - coordinate of the point \((5,100)\), neither slope (10) nor y - intercept (50)

Answer:

• For 0: Neither
• For 5: Neither
• For 10: Slope
• For 50: y - intercept
• For 100: Neither

(In the table, for each value:

• 0: Select Neither
• 5: Select Neither
• 10: Select Slope
• 50: Select y - intercept
• 100: Select Neither)