Question

practice & problem solving

1. leveled practice what is the graph of the equation y = 2x + 4?

the y - intercept is , which means the line crosses the y - axis at the point (, ). plot this point.
the slope of the line is positive, so it goes from left to right.
start at the y - intercept. move up , and then move right .
you are now at the point (, ). plot this point.
draw a line to connect the two points.

1. write an equation for the line in slope - intercept form.
2. write an equation for the line in slope - intercept form.
3. the line models the cost of renting a kayak. write an equation in slope - intercept form for the line, where x is the number of hours the kayak is rented and y is the total cost of renting the kayak.
4. graph the equation y = 3x - 5.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. For $y = 2x+4$, $m = 2$ and $b = 4$. The $y$-intercept is the value of $y$ when $x = 0$, so the line crosses the $y$-axis at $(0,4)$. A positive slope means the line goes up from left to right. The slope $m=\frac{\text{rise}}{\text{run}}$, for $m = 2=\frac{2}{1}$, so we move up 2 and right 1 from the $y$-intercept.

Step2: Analyze kayak rental problem

For the kayak rental problem, the cost per hour is the slope of the line. Since it costs $12$ per hour, $m = 12$. The deposit is the initial cost when $x = 0$, so $b=6$. The equation is $y=12x + 6$ using the slope - intercept form.

Step3: Graph $y = 3x-5$

For $y = 3x-5$, the $y$-intercept $b=-5$, so the line crosses the $y$-axis at $(0,-5)$. The slope $m = 3=\frac{3}{1}$, so from the $y$-intercept $(0,-5)$ we move up 3 and right 1 to get another point on the line $(1,-2)$ and then draw the line.

Answer:

6.
The $y$-intercept is $4$, which means the line crosses the $y$-axis at the point $(0,4)$. Plot this point.
The slope of the line is positive, so it goes up from left to right.
Start at the $y$-intercept. Move up $2$, and then move right $1$.
You are now at the point $(1,6)$. Plot this point.

1. The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. The cost per hour ($m$) is $12$ and the deposit ($b$) is $6$. So the equation is $y=12x + 6$.

10.
The $y$-intercept of the equation $y = 3x-5$ is $- 5$, so the line crosses the $y$-axis at the point $(0,-5)$.
The slope of the line is $3$ (positive), so it goes up from left to right. Start at the $y$-intercept $(0,-5)$. Move up $3$ and then move right $1$, you get to the point $(1,-2)$. Plot these two points and draw a line through them.