Graphing Systems of Linear Inequalities Warmup

• A dotted line

• A solid line

• Shade up

• Shade down

Answer explanation

The equation y = \frac{3}{5}x - 4 represents a linear function. Since it is not equal to a constant, we use a dotted line to indicate that points on the line are not included. The shading is down because the line has a negative y-intercept.

Tags

CCSS.HSF-IF.C.7A

• A dotted line

• A solid line

• Shade up

• Shade down

Answer explanation

To graph the inequality \(y \ge -\frac{2}{7}x + 1\), use a solid line because the inequality includes \(\ge\). Shade up to represent all points where \(y\) is greater than or equal to the line.

Tags

CCSS.HSA.REI.D.12

• A dotted line

• A solid line

• Shade up

• Shade down

Answer explanation

When graphing y > 6, a dotted line is used because the line itself is not included in the solution. You shade up to indicate all values of y that are greater than 6.

Tags

CCSS.HSA.REI.D.12

• A dotted line

• A solid line

• Shade up

• Shade down

Answer explanation

For the inequality y < -9x, you draw a dotted line because the inequality is strict (not including the line). You shade down to represent all the points where y is less than -9x.

Tags

CCSS.HSA.REI.D.12

Which point is a solution?

• (0, 6)

• (-3, 4)

• (1, 0)

• (-4, 3)

Answer explanation

To determine which point is a solution, we check if it satisfies the equation. The point (1, 0) meets the criteria, while the others do not. Thus, (1, 0) is the correct solution.

Tags

CCSS.HSA.REI.D.12

Which of the following is not a solution to this system of inequalities?

• (0,-1)

• (0,3)

• (4,0)

• (6,-2)

Answer explanation

The point (0,-1) does not satisfy the system of inequalities, as it lies below the x-axis, while the other points (0,3), (4,0), and (6,-2) do satisfy the inequalities.

Tags

CCSS.HSA.REI.D.12