Question

y = -3x - 4

click to select points on the graph.

Explanation:

Identify the y-intercept

Using the Slope-Intercept Form of a linear equation, \(y = mx + b\), we identify the key parameters.
For the given equation:

$$y = -3x - 4$$

The y-intercept \(b\) is \(-4\). This corresponds to the point \((0, -4)\) on the coordinate plane.

Use the slope to find a second point

Using the Slope-Intercept Form, the slope \(m\) is \(-3\), which can be written as:

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

Starting from the y-intercept \((0, -4)\), we move down 3 units and right 1 unit to find a second point:

$$(0 + 1, -4 - 3) = (1, -7)$$

Alternatively, we can write the slope as \(\frac{3}{-1}\), moving up 3 units and left 1 unit:

$$(0 - 1, -4 + 3) = (-1, -1)$$

Verify the points on the line

Using Graphing Linear Equations, we substitute the coordinates of our points back into the equation to verify they are correct.
For \((-1, -1)\):

$$-1 = -3(-1) - 4 \implies -1 = 3 - 4 \implies -1 = -1$$

For \((1, -7)\):

$$-7 = -3(1) - 4 \implies -7 = -3 - 4 \implies -7 = -7$$

Both points are correct and can be selected to graph the line.

Answer:

To graph the equation \(y = -3x - 4\), select any two points that lie on the line. Two convenient points to select on the grid are:

• \((0, -4)\) (the y-intercept)
• \((-1, -1)\) or \((1, -7)\)