Question

practice & problem solving

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

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.
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.

kayak rentals
cost (in dollars)

1. graph the equation y = 3x - 5.

Explanation:

Step1: Identify slope and y - intercept for problem 7

The cost per hour is the slope and the deposit is the y - intercept. So \(m = 12\), \(b = 6\) and \(y=mx + b\) gives \(y = 12x+6\).

Step2: Find slope and y - intercept for problem 8

Find two points on the line to calculate slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\), and identify y - intercept when \(x = 0\) to write the equation \(y=mx + b\).

Step3: Graph the line for problem 10

First, identify the y - intercept \((0,b)\) from the equation \(y=mx + b\). Then use the slope \(\frac{\text{rise}}{\text{run}}\) to find another point and draw the line.

Answer:

1. Let's assume the slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

• Given the rent is \(12\) per hour (slope \(m = 12\)) and a \(6\) deposit (y - intercept \(b=6\)). The equation is \(y = 12x+6\).

1. For the line in the graph, find two points on the line. Let's say when \(x = 0\), \(y=- 4\) (y - intercept), and when \(y = 0\), \(x = 2\). The slope \(m=\frac{0 - (-4)}{2-0}=2\). The equation in slope - intercept form is \(y = 2x - 4\).

10.

• The y - intercept of \(y = 3x-5\) is \(-5\), so the line crosses the y - axis at the point \((0,-5)\).
• The slope of the line is \(3=\frac{3}{1}\). Starting at the y - intercept \((0, - 5)\), move up \(3\) units and then move right \(1\) unit. You will be at the point \((1,-2)\). Plot the points \((0,-5)\) and \((1,-2)\) and draw a line through them.