Question

A spring stretches in relation to the weight hanging from it according to the weight hanging from it according to the equation y = 0.75x + 0.25 where x is the weight in pounds and y is the length of the spring in inches.

How to graph the equation including axis labels
How to interpret the slope and the y-intercept of the line

Answer 1

Draw a set of coordinate axes. Label the horiz. axis "x" (to represent weight) and label the vert. axis "y" (to represent length of the spring).

y= spring length = 0.75x + 0.25 (measured in inches).
First, let x=0. y will then be 0.75(0) + 0.25. This is your "vertical intercept."
Now position your pencil on that point (0,0.25). Move your pencil point 1.00 unit to the right from (0,0.25) and then up 0.75 unit. This is what the "slope" means: rise over run. Here the rise is 0.75 and the run is 1.00.

The slope, 0.75, tells us by how much more the spring stretches as 1 more lb of weight is added to the weight already hanging from the spring.

Answer 2

Answer and Explanation:

Given : A spring stretches in relation to the weight hanging from it according to the equation
`y = 0.75x + 0.25` where x is the weight in pounds and y is the length of the spring in inches.

To find :

1) How to graph the equation including axis labels ?

2) How to interpret the slope and the y-intercept of the line?

Solution :

Linear equation
`y = 0.75x + 0.25`

1) To draw the graph we find the x and y-intercept of the line,

x- intercept i.e. y=0

`0.75x + 0.25=0`

`0.75x=-0.25`

`x=-(0.25)/(0.75)`

`x=-0.33`

y- intercept i.e. x=0

`y=0.75(0) + 0.25`

`y=0.25`

Plotting these two points (-0.33,0) and (0,0.25).

Refer the attached figure below.

2) The general form of line is
`y=mx+c`

where, m is the slope and b is the y-intercept of the line.

Comparing with given line
`y = 0.75x + 0.25`

The slope of the line is m=0.75

and the y-intercept of the line is b=0.25.