Mathematics
Grade 7
15 min
Graph a line using slope
Graph a line using slope
Tutorial Preview
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.
Interpret slope as 'rise over run' to find additional points on a line.
Accurately graph a straight line given its slope and y-intercept.
Understand how the sign of the slope affects the direction of the line.
Draw a complete line with arrows extending through the coordinate plane.
Ever wonder how engineers design ramps or roller coasters to have just the right steepness? 🎢 It's all about understanding how lines 'slope' up or down!
In this lesson, you'll discover how to draw straight lines on a graph using two powerful pieces of information: where the line crosses the y-axis (its starting point) and...
2
Key Concepts & Vocabulary
TermDefinitionExample
Coordinate PlaneA flat surface formed by two intersecting number lines, the x-axis (horizontal) and y-axis (vertical), used to locate points.The grid system where you plot points like (2, 3).
Ordered PairA pair of numbers (x, y) that gives the location of a point on the coordinate plane, where x is the horizontal position and y is the vertical position.The point (3, 5) means 3 units right from the origin and 5 units up.
Y-interceptThe point where a line crosses the y-axis. At this point, the x-coordinate is always 0.If a line crosses the y-axis at 4, the y-intercept is (0, 4).
SlopeA measure of the steepness and direction of a line. It describes how much the line rises or falls vertically for every unit it moves horizontally.A slope of 2/3 means the line goes up 2 un...
3
Core Formulas
Slope-Intercept Form of a Linear Equation
$y = mx + b$
This is the most common way to write a linear equation for graphing. 'm' represents the slope of the line, and 'b' represents the y-intercept (the y-coordinate where the line crosses the y-axis).
Slope as Rise Over Run
$m = \frac{\text{rise}}{\text{run}}$
This formula tells you how to move from one point on the line to another. 'Rise' is the vertical change (up or down), and 'run' is the horizontal change (right or left). A positive rise means moving up, a negative rise means moving down. A positive run means moving right, a negative run means moving left.
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Challenging
A student graphs the line y = -1/2x + 3. They correctly plot the y-intercept at (0, 3). Then, they move down 1 unit and left 2 units. What was their error?
A.They should have moved up 1 unit.
B.They should have moved right 2 units.
C.They should have started at the origin.
D.They confused the rise and run.
Challenging
Which statement accurately describes the graph of y = -3x + 2?
A.line that crosses the y-axis at 2 and goes down 3 units for every 1 unit it moves to the right.
B.line that crosses the y-axis at -3 and goes up 2 units for every 1 unit it moves to the right.
C.line that crosses the y-axis at 2 and goes down 1 unit for every 3 units it moves to the right.
D.line that crosses the y-axis at 3 and goes down 2 units for every 1 unit it moves to the right.
Challenging
A line is graphed by starting at the point (0, -1) and then moving up 4 units and right 1 unit to find the next point. What is the equation of this line?
A.y = (1/4)x - 1
B.y = -x + 4
C.y = 4x - 1
D.y = 4x + 1
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