Question

q6: \\((-3, -5)\\) \\(m = \frac{3}{2}\\)

Explanation:

Identify the given point and slope

We are given a point and a slope to graph.

• Given point: \(P(-3, -5)\)
• Given slope: \(m = \frac{3}{2}\)

Plot the starting point

Using Graphing Linear Equations, we begin by plotting the given point.

• Locate \(-3\) on the horizontal \(x\)-axis.
• Move down \(5\) units along the vertical \(y\)-axis.
• Plot the starting point at \((-3, -5)\).

Use the slope to find a second point

The slope \(m = \frac{\text{rise}}{\text{run}} = \frac{3}{2}\) guides our next step.

• Rise is \(+3\): move up \(3\) units from \(y = -5\) to \(y = -2\).
• Run is \(+2\): move right \(2\) units from \(x = -3\) to \(x = -1\).
• Plot the second point at \((-1, -2)\).

Find an additional point for accuracy

We can repeat the slope step to find another point.

• From \((-1, -2)\), rise \(3\) units up to \(y = 1\).
• Run \(2\) units right to \(x = 1\).
• Plot the third point at \((1, 1)\).

Draw the line through the points

Connect the plotted points with a straight line.

• Draw a line passing through \((-3, -5)\), \((-1, -2)\), and \((1, 1)\).
• Extend the line across the coordinate plane with arrows.

Answer:

To graph the line:

1. Plot the starting point at \((-3, -5)\).
2. Use the slope \(m = \frac{3}{2}\) (rise \(3\), run \(2\)) to plot a second point at \((-1, -2)\).
3. Draw a straight line passing through these points.