Problem

For \(y=3x+2\) and a graph that moves right \(1\) and up \(3\), compare the equation slope with the graph's rise over run. State whether they match, the line's direction, and its \(y\text{-}\text{intercept}\).

Source parameter display: For y=3x+2, a graph description says the line moves right 1 and up 3. Which statement correctly compares the equation and graph? No requested evaluation or match verdict is annotated.

Big Picture

What this problem is really about

An equation and a graph encode the same line in different ways. Read the coefficient of the input as the equation’s slope, compute signed rise over run from the graph, and compare those rates; keep the constant term separate as the vertical intercept and use the slope’s sign for direction.

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The equation slope is 2, the graph slope is 3, and the slopes do not match; the line is increasing with y-intercept 3.

The equation slope is 3, the graph slope is 3/1=3, and the slopes do not match; the line is decreasing with y-intercept 2.

The equation slope is 3, the graph slope is 1/3, and the slopes do not match; the line is increasing with y-intercept 2.

The equation slope is 3, the graph slope is 3/1=3, and the slopes match; the line is increasing with y-intercept 2.

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For \(y=3x+2\) and a graph that moves right \(1\) and up \(3\), compare the equation slope with the graph's rise over run. State whether they match, the line's direction, and its \(y\text{-}\text{intercept}\).

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