Algebra: Solving Linear Inequalities with Two Variables

Mr. Boyd teaches how to solve linear inequalities with two variables by graphing them. The lesson covers converting equations to slope-intercept form, graphing lines, and determining whether to use solid or dashed lines. Several examples are provided, including graphing inequalities like y > 1/4x + 2 and 3x + 2y ≥ 6. The video also includes word problems, such as calculating combinations of sodas and chips under a budget and a fundraiser for a basketball team. The lesson emphasizes testing points and shading regions to represent solutions.

What is the first step in solving a linear inequality with two variables?

• Convert the equation to slope-intercept form

• Find the y-intercept

• Convert the equation to standard form

• Find the x-intercept

When graphing the inequality y > 1/4x + 2, what type of line should be used?

• Solid line

• Dotted line

• No line

• Thick line

In the inequality y < -x + 5, what is the slope of the line?

• -1

• 1

• 0

• 5

What is the slope of the line in the inequality y < -x + 5?

• 1

• -1

• 0

• 5

When graphing y < -x + 5, which region should be shaded?

• On the line

• Above the line

• Below the line

• No shading

For the inequality 3x + 2y ≥ 6, what is the y-intercept after converting to slope-intercept form?

• 3

• 0

• 6

• 2

In the inequality 3x + 2y ≥ 6, what happens to the inequality sign when dividing by a negative number?

• It flips

• It stays the same

• It disappears

• It becomes an equal sign

In the word problem involving soda and chips, what is the inequality representing the total cost?

• s + 2c < 20

• s + c > 20

• s + c < 20

• s + 2c > 20

In the word problem about brownies, what is the inequality for raising at least $600?

• 20P + 2S < 600

• 20P + 2S > 600

• 20P + 2S ≥ 600

• 20P + 2S ≤ 600

What is the y-intercept in the inequality y ≥ -10P + 300?

• 0

• -10

• 300

• 10