Question

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

Answer 1

Answer:

$y = -\frac{2}{3}x + 490$

gradient = = $-\frac{2}{3}$

y-intercept = $490$

Step-by-step explanation:

• The slope-intercept form of an equation takes the general form:

$\boxed{y = mx + c}$,

where:

m = slope,

c = y-intercept.

• We are given the equation:

$2x + 3y = 1470$

To change this into the slope-intercept form, we must make y the subject:

$3y = -2x + 1470$          [subtract $2x$ from both sides]

⇒ $y = -\frac{2}{3}x + \frac{1479}{3}$        [divide both sides by 3]

⇒ $y = -\frac{2}{3}x + 490$

• Comparing this equation with the general form equation, we see that:

m = $-\frac{2}{3}$

c = $490$.

This means that the gradient is $\bf -\frac{2}{3}$, and the y-intercept is $\bf 490$.