Question

98 = x intercept -2 \\(m = \frac{3}{4}\\)

Explanation:

Identify the given information

We are given:

• The x-intercept is \(-2\).
• The slope \(m\) is \(\frac{3}{4}\).

Find the starting point

Using the Graphing Linear Equations concept:

• An x-intercept of \(-2\) means the line crosses the x-axis at the point \((-2, 0)\).
• This gives us our first point on the coordinate plane: \(P_1 = (-2, 0)\).

Use slope to find a second point

Using the Graphing Linear Equations concept:

• Slope \(m = \frac{\text{rise}}{\text{run}} = \frac{3}{4}\).
• From \((-2, 0)\), move up 3 units (rise) and right 4 units (run).
• New x-coordinate: \(-2 + 4 = 2\).
• New y-coordinate: \(0 + 3 = 3\).
• This gives our second point: \(P_2 = (2, 3)\).

Draw the line

Using the Graphing Linear Equations concept:

• Plot the points \((-2, 0)\) and \((2, 3)\) on the grid.
• Draw a straight line passing through both points.

Answer:

To graph the line:

1. Plot the x-intercept point at \((-2, 0)\).
2. From \((-2, 0)\), use the slope \(m = \frac{3}{4}\) by moving up 3 units and right 4 units to plot the second point at \((2, 3)\).
3. Draw a straight line passing through both points.