Mathematics
Grade 7
15 min
Graph a line using slope
Graph a line using slope
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1
Introduction & Learning Objectives
Learning Objectives
Identify the slope and y-intercept from a linear equation in slope-intercept form.
Plot the y-intercept on a coordinate plane.
Use the slope (rise over run) to find additional points on a line.
Accurately draw a straight line through plotted points.
Graph a linear equation given in slope-intercept form.
Explain the meaning of positive and negative slopes in terms of direction.
Ever wondered how roller coasters are designed or how architects plan ramps? 🎢 It all starts with understanding how to graph lines and their slopes!
In this lesson, you'll learn a powerful method to draw straight lines on a graph using two key pieces of information: the slope and the y-intercept. This skill is fundamental for understanding how quantities change together and p...
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Key Concepts & Vocabulary
TermDefinitionExample
Coordinate PlaneA two-dimensional surface formed by two perpendicular number lines, the x-axis (horizontal) and the y-axis (vertical), used to locate points.The grid paper you use for graphing is a coordinate plane.
Ordered PairA pair of numbers (x, y) that specifies the location of a point on a coordinate plane, where 'x' is the horizontal distance from the origin and 'y' is the vertical distance.The point (2, 3) means move 2 units right from the origin, then 3 units up.
SlopeA measure of the steepness and direction of a line, calculated as the 'rise' (vertical change) divided by the 'run' (horizontal change) between any two points on the line.A slope of 2/3 means for every 3 units you move right, you move 2 units up.
Y-interc...
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Core Formulas
Slope Formula (Rise over Run)
$$m = \frac{\text{rise}}{\text{run}} = \frac{\Delta y}{\Delta x}$$
This formula defines slope 'm' as the change in the y-coordinates (rise) divided by the change in the x-coordinates (run) between any two points on a line. Use it to find the slope or to move from one point to another on the line.
Slope-Intercept Form
$$y = mx + b$$
This is the standard form for a linear equation where 'm' represents the slope of the line and 'b' represents the y-coordinate of the y-intercept (the point (0, b)). This form is ideal for graphing because it directly gives you a starting point and a direction.
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Challenging
Which of the following provides a complete and correct set of steps to graph the equation y = -x + 4?
A.Start at the origin. Move down 1, right 1. Draw the line.
B.Start at (0, 4). Move up 1, left 1. Draw a straight line through the points with arrows.
C.Start at (0, 4). Move down 1, right 1. Draw a line segment between the two points.
D.Start at (4, 0). Move down 1, right 1. Draw the line.
Challenging
A student is graphing y = (-2/3)x + 1. They plot the y-intercept at (0, 1). Then, they move from (0, 1) to a new point at (3, -1). Finally, they draw a line with arrows through these points. Which statement best evaluates their work?
A.They made a mistake; the second point should be at (-3, 3).
B.They made a mistake; the slope should be up 2 and right 3.
C.Their work is completely correct.
D.They made a mistake; they should have started at (1, 0).
Challenging
The line for the equation y = mx + b passes through (0, -5) and (4, -3). What steps would you take to find a third point on this line?
A.Start at (4, -3), then move down 2 and right 4.
B.Start at (0, -5), then move up 1 and right 2.
C.Start at (4, -3), then move up 1 and right 2.
D.Start at the origin, then move up 2 and right 4.
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