Question

question
graph the following features:

• y - intercept = 8
• slope = $-\frac{3}{4}$

Explanation:

1. Plot the \( y \)-intercept: The \( y \)-intercept \( (0, 8) \) is the starting point on the \( y \)-axis.
2. Use the slope: The slope \( -\frac{3}{4} \) tells us the direction and steepness of the line. A negative slope means the line is decreasing from left to right.
3. Draw the line: Connecting the plotted points with a straight line gives the graph of the line with the given \( y \)-intercept and slope.

Answer:

To graph the line with \( y \)-intercept \( = 8 \) and slope \( = -\frac{3}{4} \):

Step 1: Plot the \( y \)-intercept

The \( y \)-intercept is the point where the line crosses the \( y \)-axis. For \( y \)-intercept \( = 8 \), we plot the point \( (0, 8) \) on the coordinate plane.

Step 2: Use the slope to find another point

The slope \( m = -\frac{3}{4} \) can be interpreted as \( \frac{\text{rise}}{\text{run}} = \frac{-3}{4} \). Starting from the \( y \)-intercept \( (0, 8) \):

• Rise: Move down 3 units (because the numerator is -3, indicating a downward movement) from \( (0, 8) \). This takes us to \( (0, 8 - 3) = (0, 5) \).
• Run: Move right 4 units (because the denominator is 4, indicating a rightward movement) from \( (0, 5) \). This takes us to \( (0 + 4, 5) = (4, 5) \).

Step 3: Draw the line

Now that we have two points \( (0, 8) \) and \( (4, 5) \), we can draw a straight line passing through these two points. This line represents the equation \( y = -\frac{3}{4}x + 8 \) (since the slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept).

(Note: If you want to verify, you can find more points using the slope. For example, from \( (4, 5) \), moving down 3 and right 4 gives \( (8, 2) \), and moving up 3 and left 4 from \( (0, 8) \) gives \( (-4, 11) \), all of which lie on the same line.)