Question

Part A: Valeria walks 1.5 meters per second. Graph the relationship on the coordinate plane.Part B: What is the slope of the line representing the relationship?

Answer 1

To graph the relationship between Valeria's speed and time, plot the speed as the y-coordinate and time as the x-coordinate. The slope of the line representing the relationship is 1.5.

Step-by-step explanation:

To graph the relationship between Valeria's speed and time, we can plot the speed as the y-coordinate and time as the x-coordinate on a coordinate plane. Since Valeria walks at a constant speed of 1.5 meters per second, the graph would be a straight line with a slope of 1.5. The y-intercept of the line would be 0, indicating that Valeria starts at a speed of 0 meters per second.

The slope of the line representing the relationship is 1.5. The slope represents the rate of change of the y-coordinate (speed) with respect to the x-coordinate (time), in this case, the change in speed per unit change in time.

Answer 2

ANSWER and EXPLANATION

Part A:

We are given that Valeria walks 1.5 meters per second.

Let the amount of time spent walking be x.

Let the distance walked (in meters) be y.

There is a proportional relationship between the distance walked and the time taken.

A proportional relationship is given generally as:

y = kx

where k = constant of proportion.

From the question, the constant of proportion is 1.5 meters per second.

This implies that the equation representing the distance walked is:

y = 1.5x

We can use the equation above to plot the graph by picking at least two values of x and solving for y.

That way, we have two points to plot the graph with.

Let us find y when x is 2 and 6.

When x = 2 seconds:

y = 1.5 * 2

y = 3 meters

When x = 6 seconds:

y = 1.5 * 6

y = 9 meters

Now, we have two points (x, y) to plot with: (2, 3) and (6, 9)

Let us plot the graph:

That is the graph on the coordinate plane.

Part B:

The slope of a line is the rate of change of the line or the rate of change of the y values with respect to the rate of change of the x values.

The equation representing the relationship given above is a linear equation.

A linear equation is generally given as:

y = mx + c

where m = slope

c = y intercept

Therefore, comparing this with the equation, we see that the slope of the line representing the relationship is 1.5 meters per second.