Math Problem Statement

Complete the table and then graph the function.

y

=

1

2

x

5

x

y

10

4

0

8

10

Click to select points on the graph.

Solution

Let's complete the table and then discuss how to graph the function y=12x5y = -\frac{1}{2}x - 5.

Step 1: Calculate the yy-values

Given the function y=12x5y = -\frac{1}{2}x - 5:

  • When x=10x = -10: y=12(10)5=55=0y = -\frac{1}{2}(-10) - 5 = 5 - 5 = 0

  • When x=4x = -4: y=12(4)5=25=3y = -\frac{1}{2}(-4) - 5 = 2 - 5 = -3

  • When x=0x = 0: y=12(0)5=05=5y = -\frac{1}{2}(0) - 5 = 0 - 5 = -5

  • When x=8x = 8: y=12(8)5=45=9y = -\frac{1}{2}(8) - 5 = -4 - 5 = -9

  • When x=10x = 10: y=12(10)5=55=10y = -\frac{1}{2}(10) - 5 = -5 - 5 = -10

Completed Table

x & y \\ \hline -10 & 0 \\ -4 & -3 \\ 0 & -5 \\ 8 & -9 \\ 10 & -10 \\ \end{array}$$ ### Step 2: Graph the Function The points to plot on the graph are: - $$(-10, 0)$$ - $$(-4, -3)$$ - $$(0, -5)$$ - $$(8, -9)$$ - $$(10, -10)$$ These points will form a straight line, as the function is linear with a slope of $$-\frac{1}{2}$$. To graph: 1. Plot each of the points on a coordinate plane. 2. Draw a straight line that passes through all the plotted points. Would you like further details on how to plot the points, or do you have any other questions? ### Related Questions: 1. What does the slope of $$-\frac{1}{2}$$ indicate about the direction of the line? 2. How do you find the $$x$$-intercept of the function $$y = -\frac{1}{2}x - 5$$? 3. What is the significance of the $$y$$-intercept in this function? 4. How would the graph change if the function were $$y = \frac{1}{2}x - 5$$ instead? 5. How do you graph a function if given only the slope and $$y$$-intercept? **Tip:** When working with linear equations, identifying the slope and intercepts can help you quickly sketch the graph.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear equations
Graphing functions

Formulas

-

Theorems

-

Suitable Grade Level

Grades 7-9