Question

isaiah has $80 to order shirts for some of his family members. the linear equation $y = -10x + 80$ represents the amount of money remaining, $y$, after isaiah orders $x$ shirts. graph the equation.

Explanation:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=- 10x + 80\), when \(x = 0\), \(y=80\). So the y - intercept is \((0,80)\).

Step2: Identify the slope

The slope \(m=-10\), which can be written as \(\frac{- 10}{1}\). This means for every 1 unit we move to the right (increase in \(x\) by 1), we move down 10 units (decrease in \(y\) by 10).

Step3: Find another point

Using the slope from the y - intercept \((0,80)\), if we move \(x = 1\) (1 unit to the right), then \(y=80-10 = 70\). So another point is \((1,70)\). We can also find the x - intercept by setting \(y = 0\):
\[

$$\begin{align*} 0&=-10x + 80\\ 10x&=80\\ x&=8 \end{align*}$$

\]
So the x - intercept is \((8,0)\).

Step4: Graph the line

Plot the points \((0,80)\) and \((8,0)\) (or other points we found like \((1,70)\), \((2,60)\) etc.) and draw a straight line through them.

To graph:

• Plot the y - intercept \((0,80)\) on the y - axis.
• Plot the x - intercept \((8,0)\) on the x - axis.
• Draw a straight line connecting these two points (and extending slightly beyond, but within the context of the graph where \(x\geq0\) and \(y\geq0\) since we can't order a negative number of shirts or have negative money remaining).

(Note: Since the problem asks to graph the equation, the final answer is the graph with the line passing through \((0,80)\) and \((8,0)\) (or other valid points from the linear equation) on the given coordinate plane.)

Answer:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=- 10x + 80\), when \(x = 0\), \(y=80\). So the y - intercept is \((0,80)\).

Step2: Identify the slope

The slope \(m=-10\), which can be written as \(\frac{- 10}{1}\). This means for every 1 unit we move to the right (increase in \(x\) by 1), we move down 10 units (decrease in \(y\) by 10).

Step3: Find another point

Using the slope from the y - intercept \((0,80)\), if we move \(x = 1\) (1 unit to the right), then \(y=80-10 = 70\). So another point is \((1,70)\). We can also find the x - intercept by setting \(y = 0\):
\[

$$\begin{align*} 0&=-10x + 80\\ 10x&=80\\ x&=8 \end{align*}$$

\]
So the x - intercept is \((8,0)\).

Step4: Graph the line

Plot the points \((0,80)\) and \((8,0)\) (or other points we found like \((1,70)\), \((2,60)\) etc.) and draw a straight line through them.

To graph:

• Plot the y - intercept \((0,80)\) on the y - axis.
• Plot the x - intercept \((8,0)\) on the x - axis.
• Draw a straight line connecting these two points (and extending slightly beyond, but within the context of the graph where \(x\geq0\) and \(y\geq0\) since we can't order a negative number of shirts or have negative money remaining).

(Note: Since the problem asks to graph the equation, the final answer is the graph with the line passing through \((0,80)\) and \((8,0)\) (or other valid points from the linear equation) on the given coordinate plane.)