Question

1. open response you are selling tickets. you make $50 for signing up to sell tickets. you also make $0.75 for each ticket you sell. (lesson 5)

a. write an equation in slope - intercept form that represents how much money you make, y, for selling x tickets.

b. how much money will you make for selling 30 tickets?

1. grid graph $y = 2x - 4$ using the slope and y - intercept. (lesson 6)

1. grid consider the equation... a. graph $y = - 3$

Explanation:

Part A (Question 10A)

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value).

Step2: Identify $m$ and $b$

• The initial amount of money made for signing up is $\$50$, so $b = 50$.
• The amount of money made per ticket sold is $\$0.75$, so the rate of change (slope) $m=0.75$.
• The number of tickets sold is $x$ and the total money made is $y$.

Substituting $m = 0.75$ and $b = 50$ into the slope - intercept form, we get the equation $y=0.75x + 50$.

Step1: Substitute $x = 30$ into the equation

We have the equation $y=0.75x + 50$. Substitute $x = 30$ into this equation.

Step2: Calculate the value of $y$

First, calculate $0.75\times30$. $0.75\times30=\frac{3}{4}\times30=\frac{90}{4} = 22.5$. Then add 50 to this result: $y=22.5 + 50=72.5$.

Step1: Recall slope - intercept form for graphing

The equation is $y = 2x-4$. In slope - intercept form $y=mx + b$, $m = 2$ (slope) and $b=- 4$ (y - intercept).

Step2: Plot the y - intercept

The y - intercept is $b=-4$, so we plot the point $(0,-4)$ on the coordinate plane.

Step3: Use the slope to find another point

The slope $m = 2=\frac{2}{1}$, which means from the point $(0,-4)$, we move up 2 units (since the numerator of the slope is positive) and 1 unit to the right (since the denominator of the slope is positive). So from $(0,-4)$, moving up 2 and right 1 gives us the point $(1,-2)$. We can also move down 2 and left 1 from $(0,-4)$ to get the point $(- 1,-6)$ (but usually we use the positive slope direction for graphing).

Step4: Draw the line

Draw a straight line through the points $(0,-4)$ and $(1,-2)$ (and other points we find using the slope) to graph the line $y = 2x - 4$.

Answer:

$y = 0.75x+50$

Part B (Question 10B)