Practice reading points, plotting coordinates, finding slope, and understanding how lines appear on the coordinate plane. Coordinate geometry connects algebra to graphs and helps students prepare for functions, rates of change, and calculus.
An ordered pair tells the location of a point on the coordinate plane. It is written as (x, y). The first number is the x-coordinate, which tells how far to move left or right. The second number is the y-coordinate, which tells how far to move up or down.
Problem: Read the ordered pair (3, 2).
Step 1: Identify the x-coordinate.
The x-coordinate is 3, so move 3 units to the right.
Step 2: Identify the y-coordinate.
The y-coordinate is 2, so move 2 units up.
Answer: The point (3, 2) is located 3 units right and 2 units up.
You are ready to move on when you can explain that the first number moves left or right and the second number moves up or down.
To plot a point, start at the origin, which is the point (0, 0). Move left or right using the x-coordinate first. Then move up or down using the y-coordinate.
Problem: Plot the point (-2, 4).
Step 1: Start at the origin, (0, 0).
Step 2: The x-coordinate is -2, so move 2 units left.
Step 3: The y-coordinate is 4, so move 4 units up.
Answer: The point (-2, 4) is located 2 units left and 4 units up from the origin.
You are ready to move on when you can start at the origin, move horizontally using x, and then move vertically using y.
Slope measures how steep a line is. It compares the vertical change to the horizontal change between two points. You can remember slope as rise over run.
Problem: Find the slope between (1, 2) and (4, 8).
Step 1: Identify the two points.
(x1, y1) = (1, 2)
(x2, y2) = (4, 8)
Step 2: Use the slope formula.
m = (y2 - y1) / (x2 - x1)
Step 3: Substitute the values.
m = (8 - 2) / (4 - 1)
Step 4: Simplify.
m = 6 / 3 = 2
Answer: The slope is 2.
You are ready to move on when you can calculate vertical change, horizontal change, and write slope as rise divided by run.
Slope describes the direction and steepness of a line. A positive slope rises from left to right. A negative slope falls from left to right. A zero slope is horizontal. An undefined slope is vertical.
Problem: What type of slope does a horizontal line have?
Step 1: A horizontal line goes straight left and right.
Step 2: Its height does not change.
Step 3: Since there is no vertical change, the slope is 0.
Answer: A horizontal line has zero slope.
You are ready to move on when you can identify slope type by looking at whether a line rises, falls, stays horizontal, or stands vertical.
Slope-intercept form is one of the most common ways to write the equation of a line. It uses the form y = mx + b, where m is the slope and b is the y-intercept. The y-intercept is where the line crosses the y-axis.
Problem: Write the equation of a line with slope m = 2 and y-intercept b = -3.
Step 1: Start with slope-intercept form.
y = mx + b
Step 2: Substitute m = 2 and b = -3.
y = 2x + (-3)
Step 3: Simplify.
y = 2x - 3
Answer: y = 2x - 3
You are ready to move on when you can identify m as the slope, b as the y-intercept, and substitute both values into y = mx + b.