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Liz's math test included a survey question asking how many hours students spent studying for the test. The scatter plot below shows the relationship between how many hours students spent studying and their score on the test. A line was fit to the data to model the relationship.

Which of these linear equations best describes the given model?

(Choice A)
y=10x+20

(Choice B)
y=20x+20

(Choice C)
y=-20x+20

Based on this equation, estimate the score for a student that spent 3.8 hours studying.

Lizs math test included a survey question asking how many hours students spent studying for the test The scatter plot below shows the relationship between how m class=

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gustanika
THE LINEAR EQUATION
To determine the equation of the line, we should determine the slope of the line first. Here's the following formula to find the slope
m = [tex] \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]

The line passes through points
(x₁,y₁) = (0,20)
(x₂,y₂) = (3,80)
Therefore, the slope is
m = [tex] \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
m = [tex] \dfrac{80-20}{3-0} [/tex]
m = [tex] \dfrac{60}{3} [/tex]
m = 20

Determine the line equation
y - y₁ = m(x - x₁)
y - 20 = 20(x - 0)
y - 20 = 20x
y = 20x + 20

The linear equations best describes the given model is choice B

SCORE FOR 3.8 HOURS STUDYING
To find the score, substitute 3.8 into the coefficient x of the linear equation
y = 20x + 20
y = 20(3.8) + 20
y = 76 + 20
y = 96
The score is 96

Choice B is correct.

Straight line

It is an endless one-dimension figure that has no width. It is made by the combination of infinite points.

Given

The graph is shown.

To find

The equation of the line.

How to get the equation of the line?

We know that the equation of a line is given by y = mx + c

Here m is slope and c is constant.

[tex]\rm slope(m) = \dfrac{rise\ or\ fall}{run} \\\\slope (m) = \dfrac{20}{1} \\\\slope(m) = 20[/tex]

Then, equation will y = 20x + c

From the figure, we know the y-intercept the point will be (0, 20) from which the line is passing through. then,

[tex]\begin{aligned} \rm y &= 20x +c\\20 &= 20*0 + c\\c &= 20 \\\end{aligned}[/tex]

Then , equation will be y = 20x + 20.

Thus, choice B is correct.

More about the straight-line link is given below.

https://brainly.com/question/4695375

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