Question

homework: graph linear equations
an ice cream cone costs $5 and each additional topping
costs $0.75.

write the linear equation in slope - intercept form.

graph the linear equation using the slope and y - intercept.

graph of a coordinate plane with x - axis from 0 to 12 and y - axis from 0 to 12

explain how to graph a line using the slope and y - intercept.
first,

.
next,

Explanation:

Step1: Define variables and form equation

Let \( x \) be the number of toppings and \( y \) be the total cost. The y - intercept (cost when \( x = 0 \), i.e., no toppings) is \( 5 \), and the slope (cost per topping) is \( 0.75 \). The slope - intercept form is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. So the equation is \( y = 0.75x+5 \).

Step2: Graph using slope and y - intercept

• First, plot the y - intercept: The y - intercept \( b = 5 \), so plot the point \( (0,5) \) on the y - axis.
• Next, use the slope to find another point: The slope \( m=\frac{3}{4}\) (since \( 0.75=\frac{3}{4} \)). From the point \( (0,5) \), move up 3 units and then right 4 units (or down 3 units and left 4 units) to get the point \( (4,8) \) (or \( (- 4,2) \)). Then draw a line through the two points.

Step3: Explain graphing steps

• First, identify the y - intercept from the equation \( y = mx + b \). The y - intercept is the value of \( y \) when \( x = 0 \), so plot the point \( (0,b) \) on the coordinate plane.
• Next, use the slope \( m=\frac{\text{rise}}{\text{run}} \). Starting from the y - intercept point, move up (if rise is positive) or down (if rise is negative) by the number of units in the rise and then move right (if run is positive) or left (if run is negative) by the number of units in the run to get a second point. Then draw a straight line through the two points.

Answer:

The linear equation in slope - intercept form is \( y = 0.75x + 5 \). To graph: First, plot \( (0,5) \) (the y - intercept). Next, use the slope \( \frac{3}{4} \): from \( (0,5) \), move up 3, right 4 to get \( (4,8) \), then draw a line through these points. For the explanation: First, plot the y - intercept \( (0,b) \). Next, use the slope to find a second point and draw the line.