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

`y = -(2)/(3)x + 490`

gradient = =
`-(2)/(3)`

y-intercept =
`490`

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 = -(2)/(3)x + (1479)/(3)` [divide both sides by 3]

⇒
`y = -(2)/(3)x + 490`

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

m =
`-(2)/(3)`

c =
`490`.

This means that the gradient is
`\bf -(2)/(3)`, and the y-intercept is
`\bf 490`.