Slope is rise over run: the change in y divided by the change in x between two points on a line, m = (y₂ − y₁) ÷ (x₂ − x₁). The GED formula sheet gives this formula and both line forms, y = mx + b and point-slope. Move the two points below and watch every form update together.
The short answer
Slope is rise over run: the change in y divided by the change in x between two points on a line, m = (y₂ − y₁) ÷ (x₂ − x₁). The GED formula sheet gives this formula and both line forms, y = mx + b and point-slope. Move the two points below and watch every form update together.
What the lab does
Free and interactive, with original practice items. Practice mode gives feedback on each step; test style asks for every answer first, then shows the result and the worked steps. Goes with GEDPilot lesson GP-M05, Functions and Graphs: Connect the Representations.
Finding slope from two points, a table, a graph and a rate
Writing y = mx + b and point-slope form
Finding x- and y-intercepts
Zero and undefined slopes
Parallel and perpendicular slopes
Locating points in the coordinate plane
Key facts (checked 2026-10-26)
Math share for graphs and functions (GED assessment guide): 25%
Line formulas on the GED formula sheet: slope, y = mx + b, point-slope: 3
Slope of every horizontal line: 0
Slope of every vertical line: Undefined
How do you find the slope of a line?
Pick two points on the line. Subtract the y-values to get the rise, subtract the x-values in the same order to get the run, and divide: slope = rise ÷ run. Keep the same order on top and bottom or the sign comes out wrong.
From a graph, count the run to the right and the rise up (positive) or down (negative). From a table, compare the change in y with the change in x between two rows. From a word problem, the slope is the rate: dollars per hour, gallons per minute, miles per gallon.
Line rises from left to right: positive slope.
Line falls from left to right: negative slope.
Horizontal line: slope 0 (no rise). Its equation is y = a number.
Vertical line: slope undefined (the run is 0). Its equation is x = a number.
What are y = mx + b and point-slope form?
In y = mx + b, m is the slope and b is the y-intercept, the y-value where the line crosses the y-axis. In point-slope form, y − y₁ = m(x − x₁), you plug in the slope and any one point on the line. Both forms are on the GED formula sheet, along with the slope formula.
To find b from two points: find the slope, put one point into y = mx + b and solve for b. Example: through (2, 7) and (4, 11), the slope is 4 ÷ 2 = 2. Then 7 = 2(2) + b, so b = 3 and the line is y = 2x + 3.
How do you tell if lines are parallel or perpendicular?
Parallel lines have the same slope and different y-intercepts. Perpendicular lines meet at a right angle, and their slopes are negative reciprocals: flip the fraction and change the sign. A line with slope 2/3 is perpendicular to a line with slope −3/2, and 2/3 × (−3/2) = −1. A horizontal line (slope 0) is perpendicular to a vertical line (undefined slope).
How is slope tested on the GED?
GED Testing Service's assessment guide lists algebraic problem solving with graphs and functions as 25% of the Mathematical Reasoning test. Its targets include finding slope from a graph, an equation or a table, reading a unit rate as the slope, writing the equation of a line from a slope and a point or from two points, and using slope to spot parallel and perpendicular lines.
GED.com lists select an area among the Math question types: you click a spot on a graph or image. The "select the point" tasks in this lab practise that skill. Fill-in-the-blank slope and intercept answers are practised too.
Worked sample questions (original practice, not GED test items)
A line passes through (−3, 2) and (3, −2). What is the slope of the line? Answer: B, −2/3. Rise: −2 − 2 = −4. Run: 3 − (−3) = 6. Slope = −4 ÷ 6 = −2/3. The line falls from left to right, so a negative slope makes sense. Choice C divides run by rise.
Line p has the equation y = 4x − 1. Which line is perpendicular to line p and passes through (0, 5)? Answer: C, y = −(1/4)x + 5. The slope of line p is 4. The perpendicular slope is the negative reciprocal, −1/4. The point (0, 5) is on the y-axis, so b = 5: y = −(1/4)x + 5. Choice A is parallel to line p, B only changes the sign and D only flips the number.
The total cost C, in dollars, of a gym membership after m months is C = 12m + 30. What does the 12 represent? Answer: B, The cost for each month. In C = 12m + 30, the number multiplying m is the slope: the cost goes up $12 for every month. The 30 is the y-intercept, the cost at m = 0, which is the joining fee. After one month the total is 12 + 30 = $42.
What to do next
Try every task type once: Slope from points, a table, a graph and a rate, plus parallel, perpendicular, zero and undefined slopes. Then do a test-style set.
Read lesson GP-M05 in the workspace: Functions and Graphs: Connect the Representations (included with the book or a plan; GP-M01 is the free sample).
Practise the equation moves you need for b: Finding the y-intercept is a two-step equation. The equations lab drills those moves.
Take the free GEDPilot diagnostic: 32 original questions across all four subjects show which skills need the most work. It is practice, not an official score.
Check readiness with the official practice test: Book the real Math test after a green GED Ready result (Likely to Pass, 145 to 200). Too Close to Call (134 to 144) means a little more practice first.
Is the slope formula on the GED formula sheet? Yes. The GED Mathematics formula sheet lists the slope of a line, m = (y₂ − y₁)/(x₂ − x₁), the slope-intercept form y = mx + b and the point-slope form y − y₁ = m(x − x₁). You still need to know which one fits the question.
What is the slope of a vertical line? Undefined. Every point on a vertical line has the same x-value, so the run is 0, and you cannot divide by 0. A horizontal line has a slope of 0 because its rise is 0.
How do you find a perpendicular slope? Take the negative reciprocal: flip the fraction and change its sign. A slope of 2/3 becomes −3/2, and a slope of −4 becomes 1/4. Multiplied together, perpendicular slopes give −1. Parallel lines keep the same slope.
How do I find the y-intercept from two points? Find the slope first. Then put either point into y = mx + b and solve for b. The y-intercept is the point (0, b), where the line crosses the y-axis.
What is a select-an-area question on the GED? It is a question where you click a spot on a graph, diagram or image to answer. GED.com lists select an area among the Math question types. The "select the point" tasks in this lab practise the same skill with original graphs.
How much of GED math is graphs and functions? About a quarter. GED Testing Service's assessment guide lists algebraic problem solving with graphs and functions as 25% of the Mathematical Reasoning test.
Independent preparation materials. Not affiliated with or endorsed by ACE or GED Testing Service. GED is a registered trademark owned by ACE. Practice results do not predict an official GED score, and GEDPilot does not guarantee a passing score.