Question

drag each label to the correct location on the equation. not all labels will be used.
the following graph shows a relationship between the gallons of fuel remaining in a cars gas tank and the number of miles traveled.
find the equation for the line of best fit, in the above graph:

( y = square x + square )

labels: ( -0.04 ), ( 21.15 ), ( -0.01 ), ( 16.93 ), ( -0.06 ), ( 17.3 )

Explanation:

Step1: Identify the slope-intercept form

The equation of a line is in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. From the graph, when \( x = 0 \) (miles traveled is 0), the fuel remaining \( y \) (in gallons) is the y-intercept. Looking at the graph, when \( x = 0 \), \( y \approx 17.3 \) (since the y-intercept is around 17.3 gallons).

Step2: Calculate the slope

The slope \( m \) is calculated as \( \frac{\Delta y}{\Delta x} \). Let's take two points. For example, when \( x = 0 \), \( y = 17.3 \); when \( x = 200 \), \( y \approx 9 \). So \( \Delta y = 9 - 17.3 = -8.3 \), \( \Delta x = 200 - 0 = 200 \). Then \( m=\frac{-8.3}{200}\approx - 0.0415\approx - 0.04 \). Wait, let's check another pair. When \( x = 0 \), \( y = 17.3 \); when \( x = 100 \), \( y \approx 13 \). Then \( \Delta y = 13 - 17.3=-4.3 \), \( \Delta x = 100 - 0 = 100 \), so \( m=\frac{-4.3}{100}=-0.043\approx - 0.04 \). Alternatively, looking at the labels, the slope should be negative (since as miles increase, fuel decreases). The y-intercept is around 17.3. So the equation should be \( y=-0.04x + 17.3 \) (or checking the given labels, the slope options: -0.04, -0.01, -0.06; y-intercept options: 21.15, 16.93, 17.3). So the correct slope is -0.04 and y-intercept is 17.3.

Answer:

\( y=-0.04x + 17.3 \) (So in the blanks, the first blank is -0.04, the second blank is 17.3)