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Chapter 4: Problem 4

Complete the table of values and graph each equation. $$ y=3 x-2 $$ $$ \begin{array}{c|c} \hline x & y \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline-1 & \\ \hline \end{array} $$

Short Answer

Expert verified
The completed table of values is: $$ \begin{array}{c|c} \hline x & y \\\ \hline 0 & -2 \\\ \hline 1 & 1 \\\ \hline 2 & 4 \\\ \hline-1 & -5 \\\ \hline \end{array} $$ When graphed, the line \(y = 3x - 2\) passes through points (0, -2), (1, 1), (2, 4), and (-1, -5) with a slope of 3.

Step by step solution

01

Replace x-values in the equation with given values in the table

For each x value, plug it into the equation to find the corresponding y value: a) When \(x = 0\): \(y = 3 \times 0 - 2\) b) When \(x = 1\): \(y = 3 \times 1 - 2\) c) When \(x = 2\): \(y = 3 \times 2 - 2\) d) When \(x = -1\): \(y = 3 \times -1 - 2\)
02

Compute the y values for each x value

Calculate the y values and complete the table: a) When \(x = 0\), \(y = 0 - 2\) \(y = -2\) b) When \(x = 1\), \(y = 3 - 2\) \(y = 1\) c) When \(x = 2\), \(y = 6 - 2\) \(y = 4\) d) When \(x = -1\), \(y = -3 - 2\) \(y = -5\) $$ \begin{array}{c|c} \hline x & y \\\ \hline 0 & -2 \\\ \hline 1 & 1 \\\ \hline 2 & 4 \\\ \hline-1 & -5 \\\ \hline \end{array} $$
03

Plot the points and graph the equation

With the table of values complete, plot the points on a coordinate plane: a) Point A: (0, -2) b) Point B: (1, 1) c) Point C: (2, 4) d) Point D: (-1, -5) After plotting these points, draw a straight line through them to graph the equation \(y = 3x - 2\). The line will pass through all these points, going upwards and to the right with a slope of 3.

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Most popular questions from this chapter

Write an equation of the line perpendicular to the given line and containing the given point. Write the answer in slope-intercept form or in standard form, as indicated. $$2 x+5 y=11 ;(4,2) ; \text { standard form }$$

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