Question

the equation $y = -2x + 8$ represents the amount $y$ (in fluid ounces) of dish detergent in a bottle after $x$ days of use.

Explanation:

Assuming the problem is to graph the line \( y = -2x + 8 \) (since it's a graphing task with the equation given), here's the step - by - step for finding two points to plot:

Step 1: Find the y - intercept

The equation of a line in slope - intercept form is \( y=mx + b \), where \( b \) is the y - intercept. For the equation \( y=-2x + 8 \), when \( x = 0 \), we substitute \( x = 0 \) into the equation.
\( y=-2(0)+8=8 \). So one point on the line is \( (0,8) \).

Step 2: Find another point using the slope

The slope \( m=-2=\frac{-2}{1} \), which means for a change of \( 1 \) unit in \( x \) (increase), \( y \) changes by \( - 2 \) units (decrease). Starting from the y - intercept \( (0,8) \), if we take \( x = 1 \), then we substitute \( x = 1 \) into the equation \( y=-2x + 8 \).
\( y=-2(1)+8=6 \). So another point on the line is \( (1,6) \). We can also find the x - intercept by setting \( y = 0 \).
\( 0=-2x + 8 \)

Step 3: Solve for x (finding x - intercept)

Add \( 2x \) to both sides of the equation \( 0=-2x + 8 \): \( 2x=8 \)
Divide both sides by \( 2 \): \( x = 4 \). So the x - intercept is \( (4,0) \).

To graph the line, we plot the points \( (0,8) \) (on the y - axis) and \( (4,0) \) (on the x - axis) or \( (1,6) \) and then draw a straight line through them.

If the question was about finding when the detergent is used up (when \( y = 0 \)):

Step 1: Set \( y = 0 \) in the equation

We have the equation \( y=-2x + 8 \), set \( y = 0 \): \( 0=-2x + 8 \)

Step 2: Solve for x

Add \( 2x \) to both sides: \( 2x=8 \)
Divide both sides by \( 2 \): \( x = 4 \)

Answer:

If graphing, plot points like \( (0,8) \) and \( (4,0) \) and draw a line. If finding when detergent is used up, \( x = 4 \) days.