Question

PLEASE HELP Graph the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to x is 0.4. In other words, a change of 1 unit in x corresponds to a change of 0.4 units in y.

Graph the line and write the equation of the line.

Answer 1

Y=0.4X

Explanation:

when x=1, Y =0.4

when x=2, Y=0.8

Now you have 2 points, draw a line. voila.

see attached

Answer 2

A proportional relationship between y and x can be represented by a linear equation of the form:

y = kx

where k is the unit rate of change of y with respect to x. Given that the unit rate of change of y with respect to x is 0.4, we can substitute this value for k in the equation:

y = 0.4x

This equation represents the line that shows the proportional relationship between y and x.

To graph this equation, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. We can rewrite our equation as:

y = 0.4x + b

Since the y-intercept is the point where the line crosses the y-axis, we can substitute any value of x with 0 and solve for b

y = 0.4x + b

y = 0.4*0 + b

y = b

So the y-intercept is b = 0

Therefore, the slope-intercept form of the equation is y = 0.4x + 0

To graph the line, we can take any two x values and substitute them into the equation, and then plot the corresponding y values on the graph. For example, when x = 0, y = 0.40 + 0 = 0 and when x = 1, y = 0.41 + 0 = 0.4.

We can use these points to plot the line on a graph, it will be a straight line passing through the point (0,0) with a slope of 0.4.

Note: This line is also known as the direct variation equation.