Question

The graph below shows a line of best fit for data relating the number of marbles added in a jar to the total weight of the jar, in grams.

The line of best fit used to model the data is y = 4.95x + 160.03. Which statement is true for the graph?

A.
The slope of the line means that, on average, for every 1 gram increase in the weight of the jar, approximately 5 marbles are added to it.
B.
The slope of the line means that, on average, for every 1 marble added to the jar, the weight of the jar increases by approximately 8 grams.
C.
The y-intercept of the line means that, initially, there were about 160 marbles in the jar.
D.
The y-intercept of the line means that the weight of the empty jar is about 160 grams.

Answer 1

Answer: D.

The y-intercept of the line means that the weight of the empty jar is about 160 grams.

Explanation:

We know that the equation of line is given by
`y=mx+c`, where m is the slope of the line and c is the initial amount .

For the given linear equation
`y=4.95x+160.03`

where x is the number of marbles added, and y (dependent variable ) is the weight of the jar.

Slope of line m= 4.95 which is approximately 5 , thus, for every increase in marble, weight of jar increased by approx 5 gram.

To find the y intercept , put x=0, we get

y=160.03 which means if there is no marble then the weight of the jar = 160.03 grams or approximately 160 grams.

Thus, The y-intercept of the line means that the weight of the empty jar is about 160 grams.