Question

q5 = (-7, -4) m = \frac{4}{3}

Explanation:

Identify the given point and slope

We are given:

• A point on the line: \(P(-7, -4)\)
• The slope of the line: \(m = \frac{4}{3}\)

Plot the starting point

Using the Graphing Linear Equations concept, we first locate and plot the given point \(P(-7, -4)\) on the coordinate plane.

Find a second point using slope

Using the Slope Formula concept, we know:

$$m = \frac{\text{rise}}{\text{run}} = \frac{4}{3}$$

Starting from \((-7, -4)\):

• Move up 4 units (rise): \(-4 + 4 = 0\)
• Move right 3 units (run): \(-7 + 3 = -4\)

This gives us a second point: \((-4, 0)\).

Find a third point for accuracy

Starting from \((-4, 0)\), apply the slope again:

• Move up 4 units: \(0 + 4 = 4\)
• Move right 3 units: \(-4 + 3 = -1\)

This gives us a third point: \((-1, 4)\).

Draw the line

Using the Point-Slope Form concept, we connect the points \((-7, -4)\), \((-4, 0)\), and \((-1, 4)\) with a straight line.

Answer:

To graph the line:

1. Plot the starting point at \((-7, -4)\).
2. Use the slope \(m = \frac{4}{3}\) to find a second point by moving up 4 units and right 3 units to \((-4, 0)\).
3. Draw a straight line passing through these points.