Q1. What are the coordinates of the following points?

Background

Topic: Coordinate Geometry

This question tests your ability to read and write the coordinates of points on the Cartesian plane. Each point is represented as an ordered pair (x, y), where x is the horizontal position and y is the vertical position.

Key Terms:

• Coordinates: The pair of numbers that describe a point's location on the plane, written as (x, y).

• x-axis: The horizontal axis.

• y-axis: The vertical axis.

Step-by-Step Guidance

1. Locate each labeled point (D, E, F) on the graph.

2. For each point, count how many units it is from the origin (0, 0) along the x-axis (left/right) and y-axis (up/down).

3. Write the x-coordinate first (horizontal movement), then the y-coordinate (vertical movement), in the form (x, y).

4. Be careful with negative values: left of the origin is negative x, below the origin is negative y.

Try solving on your own before revealing the answer!

Q2. Graph

Background

Topic: Graphing Linear Equations

This question asks you to graph a linear equation in two variables. You can do this by finding two or more points that satisfy the equation and drawing a straight line through them.

Key Terms and Formulas:

• Linear Equation: An equation of the form .

• Intercepts: Where the line crosses the axes (x-intercept and y-intercept).

Step-by-Step Guidance

1. To find the y-intercept, set and solve for in .

2. To find the x-intercept, set and solve for .

3. Plot these two intercepts on the coordinate plane.

4. Draw a straight line through the two points to represent the equation.

Try solving on your own before revealing the answer!

Q3. Graph

Background

Topic: Graphing Linear Equations

This question is similar to the previous one, requiring you to graph a line by finding intercepts or other points that satisfy the equation.

Key Terms and Formulas:

• Intercepts: x-intercept (set ), y-intercept (set ).

Step-by-Step Guidance

1. Set in to find the y-intercept.

2. Set to find the x-intercept.

3. Plot both intercepts on the graph.

4. Draw a straight line through the points.

Try solving on your own before revealing the answer!

Q4. Graph

Background

Topic: Slope-Intercept Form

This question asks you to graph a line given in slope-intercept form, , where is the slope and is the y-intercept.

Key Terms and Formulas:

• Slope (m): The rate of change, rise over run.

• y-intercept (b): The value of when .

Step-by-Step Guidance

1. Identify the y-intercept () and plot the point (0, 3).

2. Use the slope to find another point: from the y-intercept, move down 3 units and right 4 units.

3. Plot the second point and draw a straight line through both points.

Try solving on your own before revealing the answer!

Q5. Find the y-intercept and slope for .

Background

Topic: Converting to Slope-Intercept Form

This question asks you to rewrite a linear equation in the form to identify the slope and y-intercept.

Key Terms and Formulas:

• Slope-Intercept Form:

• Slope (m): The coefficient of .

• y-intercept (b): The constant term.

Step-by-Step Guidance

1. Start with and solve for in terms of .

2. Isolate by subtracting from both sides.

3. Divide both sides by 4 to solve for .

4. Identify the slope () and y-intercept () from the resulting equation.

Try solving on your own before revealing the answer!