Question

equations of lines of best fit carol schoen... make an equation of the line of best fit. what does each variable represent: x: x: use the equation to predict the test score for 60 minutes studied: ____ use the equation to predict the minutes studied fo... of 72: ____ multiple-choice question the equation for this line of best fit is y = 3/2 x + 10 y = 2/3 x + 10 y = 2/3 x + 60 y = 3/2 x + 60

Explanation:

Step1: Identify two points on the line

From the graph, we can see two points: let's assume the points are \((0, 60)\) and \((30, 70)\) (we can also use other points, but these are clear). Wait, actually, looking at the grid, maybe \((0, 60)\) and \((3, 62)\)? Wait, no, let's check the slope formula. The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two clear points. From the graph, when \(x = 0\), \(y = 60\) (y-intercept, so \(b = 60\)). Then another point: when \(x = 30\), \(y = 80\)? Wait, no, maybe the points are \((0, 60)\) and \((30, 80)\)? Wait, no, let's recalculate. Wait, the options have slopes \(2/3\) or \(3/2\). Let's take two points: suppose \((0, 60)\) and \((3, 62)\) no, that's not right. Wait, the equation is in the form \(y=mx + b\). The y-intercept \(b\) is when \(x = 0\), so from the graph, when \(x = 0\), \(y = 60\), so \(b = 60\). Now, let's find the slope. Let's take another point: when \(x = 30\), what's \(y\)? Wait, maybe the points are \((0, 60)\) and \((30, 80)\)? Then slope \(m=\frac{80 - 60}{30 - 0}=\frac{20}{30}=\frac{2}{3}\). So the slope \(m=\frac{2}{3}\) and \(b = 60\), so the equation is \(y=\frac{2}{3}x+60\).

Step2: Match with the options

The options are:

1. \(y=\frac{3}{2}x + 10\)
2. \(y=\frac{2}{3}x + 10\)
3. \(y=\frac{2}{3}x + 60\)
4. \(y=\frac{3}{2}x + 60\)

We found that \(m=\frac{2}{3}\) and \(b = 60\), so the equation is \(y=\frac{2}{3}x + 60\), which is option 3 (the second option in the list? Wait, the options are:

First option: \(y = 3/2 x + 10\)

Second: \(y = 2/3 x + 10\)

Third: \(y = 2/3 x + 60\)

Fourth: \(y = 3/2 x + 60\)

So the correct one is \(y=\frac{2}{3}x + 60\), which is the third option (if we count from top: first is \(y=3/2x + 10\), second \(y=2/3x + 10\), third \(y=2/3x + 60\), fourth \(y=3/2x + 60\)). Wait, the user's options are:

1. \(y = 3/2 x + 10\)

1. \(y = 2/3 x + 10\)

1. \(y = 2/3 x + 60\)

1. \(y = 3/2 x + 60\)

So the correct equation is \(y=\frac{2}{3}x + 60\), which is the third option (the one with \(2/3x + 60\)).

Answer:

The equation of the line of best fit is \(y=\frac{2}{3}x + 60\) (the option with \(y = 2/3 x + 60\)).