Problem 8
Question
Graph each inequality. $$y>3 x+2$$
Step-by-Step Solution
Verified Answer
The graph is a dashed line starting from the \(y\)-intercept at \(y=2\), with a slope of 3. The region above the line is shaded, representing all points where \(y > 3x+2\).
1Step 1: Identifying Components
First identify the slope and the \(y\)-intercept. Here, slope \(m\) is 3 and \(y\)-intercept \(b\) is 2. So the line crosses the \(y\)-axis at \(y=2\).
2Step 2: Drawing the Line
Next, using the slope and \(y\)-intercept, draw a dashed line on a graph. Start at \(y=2\) (the y-intercept). Then, because the slope is 3, from a given point on the line, every time you move 1 unit to the right (increase \(x\) by 1), move 3 units up (increase \(y\) by 3). So, from \(y=2\), move 1 unit to the right on the \(x\)-axis and 3 units up on the \(y\)-axis to find another point.
3Step 3: Shading the Region
Since the inequality is \(y > 3x+2\), shade the area above the line, not including the line. This represents all the points \(y\) that are greater than \(3x+2\).
Other exercises in this chapter
Problem 7
Solve each system. $$\left\\{\begin{aligned} 4 x-y+2 z &=11 \\ x+2 y-z &=-1 \\ 2 x+2 y-3 z &=-1 \end{aligned}\right.$$
View solution Problem 8
write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. $$ \frac{7 x^{2}-9 x+3}{\left(x
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An objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints.
View solution Problem 8
In Exercises \(1-18,\) solve each system by the substitution method. $$ \left\\{\begin{array}{l} x^{2}+y^{2}=5 \\ 3 x-y=5 \end{array}\right. $$
View solution