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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.

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

Sagot :

Saadatkidn

Answer:

[tex]y = -\frac{2}{3}x + 490[/tex]

gradient = = [tex]-\frac{2}{3}[/tex]

y-intercept = [tex]490[/tex]

Step-by-step explanation:

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

[tex]\boxed{y = mx + c}[/tex],

where:

m = slope,

c = y-intercept.

• We are given the equation:

[tex]2x + 3y = 1470[/tex]

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

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

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

⇒ [tex]y = -\frac{2}{3}x + 490[/tex]

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

m = [tex]-\frac{2}{3}[/tex]

c = [tex]490[/tex].

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

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