Hannah is saving for a trip during the upcoming summer break. she recorded the total amount of money she had in her trip account at the end of each month. the graph shows the line of best fit for the data. the equation of the line of best fit is given below. which of the following statements is true? a) the slope of the line is 31.82, meaning that hannah initially put $31.82 into her trip account. b) the y-intercept of the line is 31.82, meaning that on average, hannah saved $31.82 each month. c) the y-intercept of the line is 92.73, meaning that hannah needed $92.73 to go on her trip. d) the slope of the line is 92.73, meaning that on average, hannah saved $92.73 each month.

D. The slope of the line is 92.73, meaning on an average, Hannah saved $92.73 each month

Step-by-step explanation:

We have the equation of the line as,

Now, as we know,

The general slope-intercept form of the straight line is y=mx+b, where m is the slope and b is the y-intercept.

On comparing, we get that,

The slope of the given line is 92.73.

Since, the slope is the average rate of change in the y-coordinates and x-coordinates.

From the question, the average rate of change is represented by the amount Hannah saved each month.

Thus, the amount Hannah saved each month is $92.73

Hence, option D is the best fit.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1