Where this sits. This is one of the five algebra families — a little over half the test, and where most students have the least ground under them. Every family page on this site has the same eight parts, in the same order, so once you know the shape of one you know the shape of all of them. Where a part is empty, it says so.
Start hereThe Coordinate PlaneIf graphs are new, begin with this page: the number line, the two axes, and plotting points, one step at a time, up to the first straight line. Then Lines on the Grid and the quiz, below.Open The Coordinate Plane → DrillsSixteen drills for this family, one skill each, ten problems at a timeGo to the drills ↓A straight line drawn on a grid, and the equation that describes it: y = mx + b, where m is the slope — how steep, and which way — and b is where the line crosses the vertical axis. Reading slope from a graph, from two points, or from a table; writing the equation from a description.
And systems, which are two lines at once and one pair of numbers that satisfies both. The everyday version of a system is two prices and two quantities: adult tickets and child tickets, sold together for one total.
What the test asks in this family
- Slope: how steep, and which wayQuiz 42 · Lines on the Grid · Lines and Functions Practice
- Slope from a graph, from two points, or from a tableQuiz 42 · Lines on the Grid · Lines and Functions Practice
- Slope as a rate in a storyQuiz 42 · Lines on the Grid
- Parallel and perpendicular linesQuiz 42 · Lines on the Grid · Lines and Functions Practice
- The x-intercept and the y-interceptQuiz 42 · Lines on the Grid · Lines and Functions Practice
- Slope-intercept form, y = mx + bQuiz 42 · Lines on the Grid · Lines and Functions Practice
- Point-slope formQuiz 42 · Lines on the Grid · Lines and Functions Practice
- Standard formQuiz 42 · Lines on the Grid · Lines and Functions Practice
- Horizontal and vertical linesQuiz 42 · Lines on the Grid · Lines and Functions Practice
- Matching an equation to a graphQuiz 42 · Lines on the Grid
- Systems: two equations at once, by substitution or eliminationQuiz 42 · Lines on the Grid · Lines and Functions Practice
All 11 have something on this site.
Seven questions across this family. Type an answer and press Check. You get the reasoning for every one, right or wrong.
- What is the slope of the line through (1, 2) and (5, 14)? 3. Slope is the rise over the run: how much the line climbs divided by how far it goes across. The y values go from 2 to 14, a rise of 12; the x values go from 1 to 5, a run of 4. 12 ÷ 4 = 3. Take the two in the same order top and bottom, or the sign comes out wrong.
- For the line y = −2x + 7, what is the slope? −2. In slope-intercept form, y = mx + b, the number multiplying x is the slope. A negative slope means the line falls as you read left to right. The sign belongs to the number, so it is −2, not 2.
- For the same line, y = −2x + 7, where does it cross the y-axis? At 7, the point (0, 7). In y = mx + b the b is the y-intercept — the value of y when x is zero. Put 0 in for x and you get y = 7, which is what crossing the vertical axis means.
- A line has a slope of 0. What kind of line is it? Horizontal. Slope zero means no rise at all, however far you run — the line is flat, with an equation like y = 3. Its opposite is a vertical line, which has no run, and dividing by zero is not allowed, so a vertical line's slope is undefined rather than zero.
- Write the equation of the line with slope 4 that crosses the y-axis at −3. y = 4x − 3. Slope-intercept form is y = mx + b, and you have been handed both: m is 4 and b is −3. This is the most useful of the three forms, because the two numbers in it are the two things a graph shows you at a glance.
- Solve the system: x + y = 10 and x − y = 2. What is x? x = 6. Adding the two equations cancels the y: (x + y) + (x − y) = 10 + 2, so 2x = 12 and x = 6. Then y = 4. That is the elimination method — use it whenever adding or subtracting the two equations makes a variable disappear.
- Line A has slope 2⁄3. Line B is parallel to it. What is line B's slope? 2⁄3. Parallel lines never meet, which is only possible if they climb at exactly the same rate — so their slopes are equal. Perpendicular is the other case: those slopes multiply to −1, so a line at right angles to this one would have slope −3⁄2.
Missed one? Quiz 42: Room for Both in Learn it covers slope, the equation of a line, parallel and perpendicular lines, and systems. The Coordinate Plane under Work it by hand starts from the beginning, and Lines on the Grid reviews this whole family, with worked examples and four sets of questions at the end. Lines and Functions Practice under On paper has 144 more.
Want more than these seven questions? Flyover I asks about all fourteen families in one sitting and ends in a grid that says where to start; Flyover II asks them again later, with different questions, so you can see what has moved.
- Quiz 42Room for BothSlope as a rate, the equation of a line in its three shapes, parallel and perpendicular lines, and systems by substitution and elimination.
One quiz and two rooms, and between them this family is complete. If the grid itself is new, start with The Coordinate Plane, in the Start here box at the top of this page, then Lines on the Grid, below; the quiz takes it from there.
Sixteen short drills, one skill each, in order. Each starts with two worked examples, then gives you ten problems (or five) and the reasoning for every answer. Each one prints, with the answer key on the last page. When you get all ten right, or all five right twice in a row, the drill gets a check mark on the Drills page.
- 13.01Slope from a graph
- 13.02Slope from two points
- 13.03Slope and y-intercept from y = mx + b
- 13.04Slope as a rate in a word problem · calculator allowed
- 13.05The x-intercept and the y-intercept
- 13.06Write y = mx + b from the slope and the y-intercept
- 13.07Write the equation from a point and the slope
- 13.08Write the equation from two points
- 13.09Standard form to slope-intercept form
- 13.10Graph a line from its equation
- 13.11Parallel and perpendicular slopes
- 13.12Horizontal and vertical lines
- 13.13Read the solution of a system off a graph
- 13.14Solve a system by substitution
- 13.15Solve a system by elimination
- 13.16System word problems: two prices, two quantities · calculator allowed
- The Coordinate Plane · start here if graphs are new: the number line, the two axes, naming and plotting points, the four quadrants, distance and the midpoint, and how points that follow a rule make a straight line. Grids to practice on, and twelve questions at the end.
- Lines on the Grid · a review of coordinate geometry: where a point lives, distance and midpoint, slope, the two intercepts, the three forms of a linear equation, and how to solve one. Worked examples throughout, seventeen questions in four sets at the end, and notes for test day.
- Lines and Functions Practice · 144 problems for families 13 and 14. For this family: slope from two points and from an equation, writing the equation of a line, intercepts, parallel and perpendicular lines, and systems of equations, with four word problems. Answer key at the end. Made to print.
- Khan Academy, math · free videos and practice. Search it for slope, slope-intercept form, graphing lines, systems of equations. These are the clips we start from in class.
- Math Antics · short, plain videos on the basics.
- Light & Salt Learning · free GED classes online, with playlists by topic.
- Get Sum Math · GED math on video, one topic at a time.
- Kaplan GED Test Prep and the McGraw-Hill Mathematical Reasoning Workbook · look up linear equations, slope, and systems in the contents of either.
On to the last one: functions and the coordinate plane. It is the same grid you have just been working on, and a function is the rule that decides which points go on it.