Math Problem Statement

Fill in the table and graph the equation y = 3x - 1.

Solution

The image you've uploaded contains a linear equation y=3x1y = 3x - 1, a table with columns for xx and yy, and a graph with axes prepared for plotting points.

Here’s how we can proceed:

Step 1: Fill the table

We will substitute different values for xx into the equation y=3x1y = 3x - 1 and compute the corresponding values of yy.

  1. If x=1x = -1: y=3(1)1=31=4y = 3(-1) - 1 = -3 - 1 = -4 So, (1,4)(-1, -4) is one point.

  2. If x=0x = 0: y=3(0)1=01=1y = 3(0) - 1 = 0 - 1 = -1 So, (0,1)(0, -1) is another point.

  3. If x=1x = 1: y=3(1)1=31=2y = 3(1) - 1 = 3 - 1 = 2 So, (1,2)(1, 2) is another point.

  4. If x=2x = 2: y=3(2)1=61=5y = 3(2) - 1 = 6 - 1 = 5 So, (2,5)(2, 5) is another point.

The table would be:

\hline x & y \\ \hline -1 & -4 \\ 0 & -1 \\ 1 & 2 \\ 2 & 5 \\ \hline \end{array}$$ ### Step 2: Plot the points on the graph Now, using the points $$(-1, -4)$$, $$(0, -1)$$, $$(1, 2)$$, and $$(2, 5)$$, you can plot them on the graph. After plotting, connect the points to form a straight line, since the equation is linear. Would you like more details on how to plot the points, or do you have any other questions? Here are 5 questions related to this concept: 1. What is the slope of the line represented by the equation $$y = 3x - 1$$? 2. How does the slope affect the steepness of the line? 3. What is the y-intercept in the equation $$y = 3x - 1$$, and how can we find it? 4. How do we know that this equation represents a linear function? 5. What would happen to the graph if the equation were $$y = -3x - 1$$? **Tip:** When graphing a linear equation, always start by plotting the y-intercept and use the slope to find other points.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing

Formulas

y = mx + b (Slope-Intercept Form)

Theorems

Slope-Intercept Form of a Line

Suitable Grade Level

Grades 7-9