Mathematics
Grade 7
15 min
Find the slope from a graph
Find the slope from a graph
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1
Introduction & Learning Objectives
Learning Objectives
Define slope as the measure of a line's steepness.
Identify two distinct points on a given line on a coordinate plane.
Accurately determine the 'rise' (vertical change) between two points on a graph.
Accurately determine the 'run' (horizontal change) between two points on a graph.
Calculate the slope of a line using the ratio of rise to run.
Interpret the sign of the slope (positive or negative) based on the line's direction.
Simplify the fractional representation of the slope to its simplest form.
Ever wondered how steep a skateboard ramp is or how quickly a mountain trail climbs? ⛰️ Mathematics gives us a special tool called 'slope' to measure exactly that!
In this lesson, you'll discover what slope is and...
2
Key Concepts & Vocabulary
TermDefinitionExample
Coordinate PlaneA two-dimensional surface formed by two perpendicular number lines, the x-axis (horizontal) and y-axis (vertical), used to locate points.Plotting the point (3, 2) on a grid where the x-axis goes left-right and the y-axis goes up-down.
Ordered PairA pair of numbers (x, y) that represents the location of a single point on a coordinate plane.The point (2, 5) means 2 units right from the origin and 5 units up.
LineA straight path that extends infinitely in both directions, often represented on a graph.The graph of y = 2x + 1 is a straight line.
RiseThe vertical change or distance between two points on a line. It's how much you move up or down.If you move from a point with y=2 to a point with y=5, the rise is 3 (5-2).
RunThe horizontal change or dista...
3
Core Formulas
Slope Formula (from a graph)
$ ext{Slope} = rac{ ext{Rise}}{ ext{Run}}$
To find the slope of a line from a graph, choose two clear points on the line. Count the vertical distance (rise) between them and the horizontal distance (run) between them. Then, divide the rise by the run. Remember to consider the direction for positive and negative values.
Determining Rise Direction
Upward movement is positive rise (+). Downward movement is negative rise (-).
When counting the vertical change between two points, if you move up from the first point to the second, the rise is positive. If you move down, the rise is negative.
Determining Run Direction
Rightward movement is positive run (+). Leftward movement is negative run (-).
When counting the horizontal change between two p...
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Challenging
A student incorrectly says the slope of the line passing through (1, 1) and (4, 7) is 2/1. Which of these is the most likely reason for their error?
A.They used Run/Rise instead of Rise/Run.
B.They made a sign error when calculating the rise.
C.They did not simplify their fraction.
D.They chose points that were not on the grid intersections.
Challenging
A line passes through the point (2, 2) and has a slope of 3. Which of the following graphs could represent this line?
A.line passing through (2, 2) and (3, 5).
B.line passing through (2, 2) and (5, 3).
C.line passing through (2, 2) and (3, -1).
D.line passing through (2, 2) and (1, 5).
Challenging
A line passes through the points (1, 2) and (3, 6). Which of the following points would also be on the same line?
A.(4, 7)
B.(4, 8)
C.(5, 9)
D.(2, 5)
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