Sal’s Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal’s profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.

Question

1. Change the equation into slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work below:

Answer 1

To change the equation \(2x + 3y = 1470\) into slope-intercept form (which is generally written as \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), we need to solve for \(y\).

Here are the steps:

1. Start with the original equation: \[ 2x + 3y = 1470 \]

2. Subtract \(2x\) from both sides to isolate the term with \(y\): \[ 3y = -2x + 1470 \]

3. Now, divide every term by 3 to solve for \(y\): \[ y = -\frac{2}{3}x + \frac{1470}{3} \]

4. Simplify \(\frac{1470}{3}\): \[ \frac{1470}{3} = 490 \]

5. Now we can write the equation in slope-intercept form: \[ y = -\frac{2}{3}x + 490 \]

Identifying the slope and y-intercept:

• The slope \(m\) is \(-\frac{2}{3}\).
• The y-intercept \(b\) is \(490\).

Summary:

• The equation in slope-intercept form is: \[ y = -\frac{2}{3}x + 490 \]
• Slope (\(m\)): \(-\frac{2}{3}\)
• y-intercept (\(b\)): \(490\)