Question

a train travels 45 miles per hour. represent the relationship between distance and time in the coordinate plane.

Explanation:

Step1: Define the relationship

The distance $d$ (miles) traveled by the train is equal to speed multiplied by time $t$ (hours). The speed is 45 mph, so the equation is:
$d = 45t$

Step2: Identify key points

Calculate distance for given time values:

• When $t=0$, $d=45\times0=0$ → Point $(0, 0)$
• When $t=1$, $d=45\times1=45$ → Point $(1, 45)$
• When $t=2$, $d=45\times2=90$ → Point $(2, 90)$
• When $t=3$, $d=45\times3=135$ → Point $(3, 135)$
• When $t=4$, $d=45\times4=180$ → Point $(4, 180)$

Step3: Plot and connect points

Plot the points on the coordinate plane (x-axis: Time (hours), y-axis: Distance (miles)), then draw a straight line through them (starting at (0,0) and extending through the calculated points).

Answer:

The relationship is represented by the linear equation $d=45t$, graphed as a straight line passing through points $(0,0)$, $(1,45)$, $(2,90)$, $(3,135)$, $(4,180)$ on the provided coordinate plane.