Question

A panel of judges was asked to judge the quality of different kinds of potato chips. The relationship between their ratings and the price of the chips is shown in the scatter plot below. A line was fit to the data to model the relationship.
Which of these linear equations best describes the given model?

Answer 1

Answer:

Equation (A) $\hat{y}=2.5 x-0.5$ describes the given model.

Step-by-step explanation:

• An equation between two variables that provides a straight bar when plotted on a diagram is called linear equations.

Step 1

The y-intercept can be a negative numeral only, as the line of adequate fit is not touching the y-axis at any positive values of y, so the y-intercept can just be - 0.5.

The slope of a line can be discovered between the two pinpoints (0.6,1) and (1,2) by the slope Equation,

$y=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Put, $x_{1}=0.6$

$y_{1}=1$

$x_{2}=1$

and $y_{2}=2$ in the formula we get,

$y=\frac{2-1}{1-0.6}$

$=\frac{1}{0.4}$

$=2.5$.

Step 2

Hence, the linear equation which best represents the conveyed example is $\hat{y}=2.5 x-0.5$.

Therefore the correct option is (A) $\hat{y}=2.5 x-0.5$.

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Answer 2

Answer:

Equation (A) $y=2.5x-0.5$ describes the given model.

Step-by-step explanation:

• The general equation of the line is $y=mx+c$
• The value of the slope $m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
• Put the value of $y_{2}= 2, y_{1} = 1, x_{2}=1, x_{1}=0.6$ (by the help of the dots on the graph given to us)
• with the help of these we get the value of $m=2.5$
• hence the equation is $y=2.5x+c$
• Now put the value of any point in this equation as it should satisfy the equation $x=0.6$ and $y = 1$ then we get the value of the y intercept c as $-0.5$
• Hence the equation now becomes $y=2.5x-0.5$