Graphing Linear Equations and Inequalities

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Questions and Answers

What is the slope of the line represented by the equation $2x - 3y = 3$?

$-\frac{2}{3}$ (correct)

$\frac{3}{2}$

$\frac{2}{3}$

$-\frac{3}{2}$

What is the y-intercept of the line given by the equation $x + 4y = 20$?

5 (correct)

Which ordered pair is a solution for the equation $3x + 5y = 0$?

(0, 0)

(-5, 3) (correct)

(5, -3)

(3, -5)

What is the x-intercept of the equation $8x - 5y = -25$?

2.5 Signup and view all the answers

Which of these points lies on the line described by $2x - 3y = 3$?

(3, 1) Signup and view all the answers

What is the result of substituting $x = 2$ in the equation $x + 4y = 20$?

5 Signup and view all the answers

Which of the following is the correct standard form for the equation of the line with a slope of $-2$ and passing through the point (0, 3)?

$x + 2y = 6$ Signup and view all the answers

For which value of $y$ does the point (3, y) satisfy the equation $3x + 5y = 0$?

-3 Signup and view all the answers

What is the feasible region for the inequality x + y ≤ 2?

A region below the line with points (0,2) and (2,0) Signup and view all the answers

Which of the following represents the graph of 4x + 5y ≥ 20?

A line intersecting at (4,0) and (0,5) Signup and view all the answers

Given the inequality x - 2y < -4, what would be the slope of the boundary line?

2 Signup and view all the answers

Which point (x,y) does NOT satisfy the inequality 7x + 3y < -6?

(-2, 1) Signup and view all the answers

Which inequality has a solution set represented by a region to the right of the line?

x - y > 1 Signup and view all the answers

For which inequality will the graph include points above the line y = -2x + 4?

y > -2x + 4 Signup and view all the answers

What does the inequality x + y ≤ 2 represent in the coordinate plane?

Points below or on the line intersecting at (2,0) and (0,2) Signup and view all the answers

Which of these inequalities will have a boundary line that is dashed?

x + y < 2 Signup and view all the answers

What is the corner point for the feasible region defined by the inequalities x + y ≤ 2 and 4x + 5y ≥ 20?

No corner point exists for these inequalities Signup and view all the answers

What is the slope of the line represented by the inequality y > -5x + 5?

-5 Signup and view all the answers

Which of the following points satisfies the inequality y > x + 2?

3 Signup and view all the answers

For the inequality y ≥ -x, which statement is true?

The line is solid and includes points on -x. Signup and view all the answers

Which inequality represents a region above the line with a slope of 1 that intersects the y-axis at 2?

y > x + 2 Signup and view all the answers

What is the y-intercept of the line represented by y ≤ x + 5?

5 Signup and view all the answers

If y > -5x + 5 is graphed, in which quadrant will it extend infinitely?

In Quadrants I and II Signup and view all the answers

What type of line is represented by the inequality y < x + 2?

Dashed line Signup and view all the answers

Which inequality creates a region below the line that has a slope of -1?

y < -x Signup and view all the answers

Which of the following correctly identifies the region of y < -x?

Below the line Signup and view all the answers

When graphing y ≥ -x, what will the shading represent?

Above the line Signup and view all the answers

What is the significance of a solid line in the graph of y ≤ x + 5?

Points on the line are included. Signup and view all the answers

For the inequality y > -5x + 5, which of the following coordinates does not satisfy it?

(3, -5) Signup and view all the answers

How would you describe the region represented by y ≤ x + 2?

On or below the line x + 2 Signup and view all the answers

What is the y-intercept of the line represented by the equation y = x?

0 Signup and view all the answers

What is the slope of the line y = -x - 5?

-1 Signup and view all the answers

Which graph represents the equation y = -x - 4?

A diagonal line starting from (0, -4) Signup and view all the answers

What type of line does the equation y = 0 represent?

A horizontal line Signup and view all the answers

What are the coordinates of the point where the line y = x intersects the x-axis?

(0, 0) Signup and view all the answers

In the equation y = -x - 5, what is the y-coordinate when x = 2?

-3 Signup and view all the answers

When graphing y = -x - 5, which point lies on the line?

(0, -5) Signup and view all the answers

What is the slope-intercept form of the line represented by y = -x - 4?

y = -x - 4 Signup and view all the answers

What is the effect of adding a positive number to the equation y = -x?

Raises the line vertically Signup and view all the answers

Which equation describes a line that will never intersect the x-axis?

y = -5 Signup and view all the answers

At which value of x will the equation y = -x - 4 have a y-value of 0?

-5 Signup and view all the answers

What is the domain of the line represented by y = 0?

All real numbers Signup and view all the answers

For the line y = -x - 4, what point is found at x = -1?

-3 Signup and view all the answers

Which line has the steepest slope among the following?

y = x Signup and view all the answers

Study Notes

Linear Equations and Inequalities

Graphing Lines: The assignment involves graphing various linear equations and inequalities on coordinate planes.
Equations: The examples provided include linear equations in various formats.
- y = -x
- y = -x - 5
- y = -x - 4
- y = 0
- 2x - 3y = 3
- x + 4y = 20
- 3x + 5y = 0
- 8x - 5y = -25
Inequalities: The assignment also introduces linear inequalities.
- y > -5x + 5
- y > -x + 2
- y ≥ -x/3
- y ≤ -x + 5
- x + y ≤ 2
- 4x + 5y ≥ 20
- x - 2y < -4
- 7x + 3y < -6

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Description

This quiz focuses on graphing various linear equations and inequalities on coordinate planes. It includes examples of linear equations and inequalities across different formats. Test your knowledge on how to accurately represent these mathematical concepts visually.

Graphing Linear Equations and Inequalities

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Podcast

Questions and Answers

What is the slope of the line represented by the equation $2x - 3y = 3$?

What is the y-intercept of the line given by the equation $x + 4y = 20$?

Which ordered pair is a solution for the equation $3x + 5y = 0$?

What is the x-intercept of the equation $8x - 5y = -25$?

Which of these points lies on the line described by $2x - 3y = 3$?

What is the result of substituting $x = 2$ in the equation $x + 4y = 20$?

Which of the following is the correct standard form for the equation of the line with a slope of $-2$ and passing through the point (0, 3)?

For which value of $y$ does the point (3, y) satisfy the equation $3x + 5y = 0$?

What is the feasible region for the inequality x + y ≤ 2?

Which of the following represents the graph of 4x + 5y ≥ 20?

Given the inequality x - 2y < -4, what would be the slope of the boundary line?

Which point (x,y) does NOT satisfy the inequality 7x + 3y < -6?

Which inequality has a solution set represented by a region to the right of the line?

For which inequality will the graph include points above the line y = -2x + 4?

What does the inequality x + y ≤ 2 represent in the coordinate plane?

Which of these inequalities will have a boundary line that is dashed?

What is the corner point for the feasible region defined by the inequalities x + y ≤ 2 and 4x + 5y ≥ 20?

What is the slope of the line represented by the inequality y > -5x + 5?

Which of the following points satisfies the inequality y > x + 2?

For the inequality y ≥ -x, which statement is true?

Which inequality represents a region above the line with a slope of 1 that intersects the y-axis at 2?

What is the y-intercept of the line represented by y ≤ x + 5?

If y > -5x + 5 is graphed, in which quadrant will it extend infinitely?

What type of line is represented by the inequality y < x + 2?

Which inequality creates a region below the line that has a slope of -1?

Which of the following correctly identifies the region of y < -x?

When graphing y ≥ -x, what will the shading represent?

What is the significance of a solid line in the graph of y ≤ x + 5?

For the inequality y > -5x + 5, which of the following coordinates does not satisfy it?

How would you describe the region represented by y ≤ x + 2?

What is the y-intercept of the line represented by the equation y = x?

What is the slope of the line y = -x - 5?

Which graph represents the equation y = -x - 4?

What type of line does the equation y = 0 represent?

What are the coordinates of the point where the line y = x intersects the x-axis?

In the equation y = -x - 5, what is the y-coordinate when x = 2?

When graphing y = -x - 5, which point lies on the line?

What is the slope-intercept form of the line represented by y = -x - 4?

What is the effect of adding a positive number to the equation y = -x?

Which equation describes a line that will never intersect the x-axis?

At which value of x will the equation y = -x - 4 have a y-value of 0?

What is the domain of the line represented by y = 0?

For the line y = -x - 4, what point is found at x = -1?

Which line has the steepest slope among the following?

Study Notes

Linear Equations and Inequalities

Studying That Suits You

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