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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.

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

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 $2 x+3 y=1,470$ 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. $\newline$ $1$ . Change the equation into slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work below:

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Find a value using two-variable equations: word problems

Full solution

Q. 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

2 x+3 y=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.

\newline

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:

Solve for y: First, we need to solve for y to get the equation into slope-intercept form, which is $y = mx + b$ . So, we'll subtract $2x$ from both sides of the equation. $2x + 3y - 2x = 1,470 - 2x$ This simplifies to $3y = -2x + 1,470$ .
Divide by $3$ : Next, we divide everything by $3$ to solve for $y$ . $y = \frac{{-2x + 1,470}}{3}$
Simplify the equation: Now, we simplify the equation by dividing each term by $3$ . $y = \left(-\frac{2}{3}\right)x + \left(\frac{1,470}{3}\right)$
Calculate y-intercept: Finally, we calculate $1,470$ divided by $3$ to find the y-intercept. $\newline$ $1,470 / 3 = 490$ $\newline$ So, the slope-intercept form of the equation is $y = (-2/3)x + 490$ .
Find slope and y-intercept: The slope of the equation is the coefficient of $x$ , which is $-\frac{2}{3}$ . The y-intercept is the constant term, which is $490$ .

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