Questions: Systems of Linear Equations Graphing a linear inequality in the plane: Slope-Intercept form Graph the inequality: y ≤ (1/3)x + 2

Transcript text: Systems of Linear Equations Graphing a linear inequality in the plane: Slope-Intercept form Graph the inequality: $y \leq \frac{1}{3}x + 2$ [Graph coordinate plane with tools for drawing] Explanation Check

Solution

Solution Steps

Step 1: Find the y-intercept

The y-intercept is the constant term in the inequality, which is 2. This means the line crosses the y-axis at the point (0, 2).

Step 2: Find the slope

The slope is the coefficient of x, which is -1/3. This means for every 3 units we move to the right along the x-axis, we move 1 unit down along the y-axis.

Step 3: Determine the type of line

Since the inequality is 'less than or equal to', ≤, we draw a solid line to indicate that points on the line are included in the solution set.

Step 4: Determine the shaded region

Since the inequality is y ≤ (-1/3)x + 2, we shade the region below the line. This represents all the points (x,y) that satisfy the inequality.