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02.c1.pre-algebra.c1dm2.3_2026
the table shows the linear relationship between the elevation, in thousands of feet, and the standard temperature in degrees fahrenheit (°f)

elevation (thousands of feet)	temperature (°f)
3.5	46.75
13	13.5
16	3

determine the slope and y-intercept of the linear relationship between x, the elevation, in thousands of feet, and y, the temperature, in degrees fahrenheit.
part a
what is the slope?

• 3.5
• 0.29
• -3.5
• -0.29

part b
what is the y-intercept?

Explanation:

Part A: Slope Calculation

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Let's take the first two points \((2, 52)\) and \((3.5, 46.75)\).

Step2: Substitute values

Substitute \( x_1 = 2 \), \( y_1 = 52 \), \( x_2 = 3.5 \), \( y_2 = 46.75 \) into the formula:
\( m = \frac{46.75 - 52}{3.5 - 2} = \frac{-5.25}{1.5} = -3.5 \)? Wait, no, wait—wait, let's check with another pair. Wait, maybe I made a mistake. Wait, let's take \((2, 52)\) and \((16, 3)\). Then \( m = \frac{3 - 52}{16 - 2} = \frac{-49}{14} = -3.5 \)? Wait, no, the options have -3.5? Wait, no, the options: 3.5, 0.29, -3.5, -0.29. Wait, maybe I miscalculated. Wait, let's recalculate with \((2, 52)\) and \((3.5, 46.75)\): \( 46.75 - 52 = -5.25 \), \( 3.5 - 2 = 1.5 \), \( -5.25 / 1.5 = -3.5 \). Wait, but the options have -3.5? Wait, no, the user's options: let's check the image. The options for Part A: 3.5, 0.29, -3.5, -0.29. Wait, maybe I messed up. Wait, no—wait, slope formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Let's take \((2, 52)\) and \((13, 13.5)\). Then \( y_2 - y_1 = 13.5 - 52 = -38.5 \), \( x_2 - x_1 = 13 - 2 = 11 \), \( -38.5 / 11 = -3.5 \). Ah, so slope is -3.5? Wait, but the options include -3.5? Wait, the user's image shows options: 3.5, 0.29, -3.5, -0.29. So the correct slope is -3.5? Wait, no, wait—wait, maybe I inverted x and y. Wait, the problem says x is elevation (thousands of feet), y is temperature. So the linear equation is \( y = mx + b \), where m is slope. So when elevation (x) increases, temperature (y) decreases, so slope should be negative. So between (2,52) and (3.5,46.75): \( m = (46.75 - 52)/(3.5 - 2) = (-5.25)/1.5 = -3.5 \). Yes, so slope is -3.5.

Part B: Y-Intercept Calculation

Step1: Use slope-intercept form

The slope-intercept form is \( y = mx + b \), where \( m = -3.5 \) (from Part A). We can use a point, say \((2, 52)\), to solve for \( b \).

Step2: Substitute values

Substitute \( x = 2 \), \( y = 52 \), and \( m = -3.5 \) into \( y = mx + b \):
\( 52 = -3.5(2) + b \)
\( 52 = -7 + b \)
Add 7 to both sides: \( b = 52 + 7 = 59 \). Let's verify with another point, e.g., \((16, 3)\): \( y = -3.5(16) + 59 = -56 + 59 = 3 \), which matches. So y-intercept is 59.

Part A Answer:

-3.5 (Option: -3.5)

Part B Answer:

59

Answer:

Step1: Use slope-intercept form

The slope-intercept form is \( y = mx + b \), where \( m = -3.5 \) (from Part A). We can use a point, say \((2, 52)\), to solve for \( b \).

Step2: Substitute values

Substitute \( x = 2 \), \( y = 52 \), and \( m = -3.5 \) into \( y = mx + b \):
\( 52 = -3.5(2) + b \)
\( 52 = -7 + b \)
Add 7 to both sides: \( b = 52 + 7 = 59 \). Let's verify with another point, e.g., \((16, 3)\): \( y = -3.5(16) + 59 = -56 + 59 = 3 \), which matches. So y-intercept is 59.

Part A Answer:

-3.5 (Option: -3.5)

Part B Answer:

59