Can you give me steps on how to do this and can you do this problem so I can figure out the rest. Thanks so much.
Directions: Graph each pair of equations. Describe any similarities or differences and explain why they are a family graph.
1. y= 3x-2
y= -x-2
Could Someone Help Me Please
for each equation make a table of values of at least two ordered pairs, then graph each line
first one:
y = 3x - 2
x y
0 -2
2 4
notice that this line has a slope of 3 and a y-intercept of -2
second one:
y = -x - 2
x y
0 -2
-4 2
this one has a slope of -1, it should lean to the left, and a y-intercept of -2
notice they intersect at (0,-2), so they would be part of a "family" of lines that pass through the common point (0,-2)
What do you mean by lean to the left
Sure! To graph each pair of equations, we will proceed with the following steps:
Step 1: Choose a range for the x-values. Start by selecting a set of x-values that will cover the desired region. For simplicity, let's choose a range of -5 to 5.
Step 2: Substitute the x-values into each equation to find the corresponding y-values. For example, if we let x = -5, we can substitute it into both equations to find the y-values.
For the first equation, y = 3x - 2:
When x = -5, y = 3(-5) - 2 = -15 - 2 = -17.
For the second equation, y = -x - 2:
When x = -5, y = -(-5) - 2 = 5 - 2 = 3.
Repeat this process for various x-values to generate multiple points for each equation.
Step 3: Plot the points on a graph. Use the x-values as the horizontal axis and the y-values as the vertical axis. Connect the points for each equation with a straight line.
By graphing the pair of equations, you can observe any similarities and differences between the two graphs.
Let's work through an example for the given pair of equations:
1. y = 3x - 2
2. y = -x - 2
Following the steps outlined above:
Step 1: We choose a range of x-values from -5 to 5.
Step 2: We substitute the x-values into each equation to find the corresponding y-values. Here's a table of selected values:
|x | y = 3x - 2 | y = -x - 2 |
|-----|------------|------------|
|-5 | -17 | 3 |
|-3 | -11 | -1 |
|0 | -2 | -2 |
|2 | 4 | -4 |
|5 | 13 | -7 |
Step 3: Plot the points on a graph and connect them with straight lines:
The graph for the equation y = 3x - 2 is a straight line that passes through the points (-5, -17), (-3, -11), (0, -2), (2, 4), and (5, 13).
The graph for the equation y = -x - 2 is also a straight line that passes through the points (-5, 3), (-3, -1), (0, -2), (2, -4), and (5, -7).
Similarities: Both graphs are straight lines.
Differences: The slopes of the lines are different. The first equation, y = 3x - 2, has a positive slope of 3, while the second equation, y = -x - 2, has a negative slope of -1.
Explanation of family graphs: The two graphs are considered a family graph because they share the same y-intercept value of -2. Although their slopes differ, their simultaneous equations have the same constant term, which leads to a common point of intersection at (0, -2). This suggests that the two lines are related or have a family resemblance.