Question

use the line tool to graph the line that contains the given point and has the given slope.
point: (0, -2)
slope: m = 3

Explanation:

Step1: Plot the given point

The given point is \((0, -2)\), which is on the y - axis (since \(x = 0\)). Locate this point on the coordinate plane.

Step2: Use the slope to find another point

The slope \(m=\frac{\text{rise}}{\text{run}} = 3=\frac{3}{1}\). This means for a run (change in \(x\)) of \(1\) unit, the rise (change in \(y\)) is \(3\) units. Starting from the point \((0, -2)\), if we move \(1\) unit to the right (increase \(x\) by \(1\)) to \(x = 1\), we move \(3\) units up (increase \(y\) by \(3\)) from \(y=-2\) to \(y=-2 + 3=1\). So another point on the line is \((1,1)\).

Step3: Draw the line

Using the line tool, draw a straight line passing through the points \((0, -2)\) and \((1,1)\) (and extending in both directions).

(Note: Since this is a graphing problem, the final answer is the graph of the line passing through \((0, - 2)\) with slope \(3\). To describe the equation of the line for reference, using the slope - intercept form \(y=mx + b\), where \(m = 3\) and \(b=-2\) (because the point \((0, - 2)\) is the y - intercept), the equation of the line is \(y = 3x-2\).)

Answer:

The line is graphed by plotting the point \((0, - 2)\) and then using the slope \(m = 3\) to find another point (e.g., \((1,1)\)) and drawing a straight line through these points. The equation of the line is \(y=3x - 2\).