Question

problems 1 - 2: here is a graph about school supplies.

1. a teacher spent $21 on packs of stickers and packs of pencils for her class.

• stickers cost $1.50 per pack.
• pencils cost $3.50 per pack.

show or explain how you know that this graph represents this situation.
1.5x + 3.5y = 21

1. circle a coordinate pair and explain what it means in this situation.

(0,6) (7,3) (14,0)

1. circle the line that represents 12 = 3x + 4y.

line a line b line c
show or explain how you know.

1. which equation is equivalent to 15x + 3y = 27

a. y = 2/3+5x b. y = 2/3 - 5x c. y = 2 - 15x d. y = 2 - 5x

1. match each equation with its equivalent equation.

a. 4x + 6y = 20 b. 3x - 6y = 16 c. 2x - 3y = 10 d. - 3x + 6y = 16
y = 8/3+1/3x y = 10/3+2/3x y = 10/3 - 2/3x y = - 8/3+1/2x

Explanation:

1.

Step1: Set up the cost - equation

Let $x$ be the number of packs of stickers and $y$ be the number of packs of pencils. The cost of stickers is $1.50x$ and the cost of pencils is $3.50y$, and the total cost is $21$. So the equation is $1.5x + 3.5y=21$.

Step2: Check the intercepts

When $x = 0$, we have $3.5y=21$, so $y=\frac{21}{3.5}=6$. This gives the point $(0,6)$ on the graph. When $y = 0$, we have $1.5x=21$, so $x=\frac{21}{1.5}=14$. This gives the point $(14,0)$ on the graph. Also, for the point $(7,3)$: $1.5\times7+3.5\times3=10.5 + 10.5=21$. So the graph represents the situation.

Let's take the coordinate pair $(7,3)$. The $x$ - coordinate represents the number of packs of stickers and the $y$ - coordinate represents the number of packs of pencils. So the point $(7,3)$ means the teacher bought 7 packs of stickers and 3 packs of pencils.

Step1: Rewrite the equation in slope - intercept form

Starting with $12 = 3x+4y$, we solve for $y$: $4y=-3x + 12$, so $y=-\frac{3}{4}x+3$.

Step2: Find the $y$ - intercept and slope

The $y$ - intercept is 3 and the slope is $-\frac{3}{4}$. Line $b$ has a $y$ - intercept of 3 and a negative slope.

Answer:

The graph represents the situation because the points on the graph satisfy the cost - equation $1.5x + 3.5y = 21$.

2.