Question

graph the following linear equation.
$y = 3x + 7$
step 2 of 3: plot the $y$-intercept of the linear equation on the graph.
answer 2 points
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Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept. The \(y\)-intercept is the point where the line crosses the \(y\)-axis, and at this point, \(x = 0\).

Step2: Identify the \(y\)-intercept from the equation

For the equation \(y=3x + 7\), comparing it with \(y=mx + b\), we can see that \(b = 7\). So the \(y\)-intercept is the point \((0,7)\).
To plot the \(y\)-intercept, we need to find the point on the \(y\)-axis (where \(x = 0\)) with \(y\)-coordinate \(7\). On the given graph, we move along the \(y\)-axis (the vertical axis) to the value \(y = 7\) (since \(x = 0\) for the \(y\)-intercept) and mark that point.

Answer:

The \(y\)-intercept of the line \(y = 3x+7\) is the point \((0,7)\), so we plot the point \((0,7)\) on the graph (on the \(y\)-axis at \(y = 7\)).