Question

graph a line given a point and slope

q3: \\((2, 5)\\), \\(m = -\frac{1}{3}\\)

Explanation:

Identify the given point and slope

We are given:

• Point: \((2, 5)\)
• Slope: \(m = -\frac{1}{3}\)

Plot the starting point

Using the Graphing Linear Equations concept, we first plot the given point \((2, 5)\) on the coordinate plane.

Find a second point using slope

Using the Slope Formula concept, we know:

$$ m = \frac{\text{rise}}{\text{run}} = \frac{-1}{3} $$

From \((2, 5)\), move down \(1\) unit and right \(3\) units:

$$ (2 + 3, 5 - 1) = (5, 4) $$

Find a third point for accuracy

Alternatively, we can move up \(1\) unit and left \(3\) units:

$$ (2 - 3, 5 + 1) = (-1, 6) $$

Draw the line

Connect the points \((-1, 6)\), \((2, 5)\), and \((5, 4)\) with a straight line.

Answer:

To graph the line:

1. Plot the starting point at \((2, 5)\).
2. Use the slope \(m = -\frac{1}{3}\) (down \(1\) unit, right \(3\) units) to plot a second point at \((5, 4)\).
3. Draw a straight line passing through both points.