Interpret and graph lines through slope, intercepts, and special cases.
Common Core8.EE.B.5F-IF.B.4F-IF.C.7aF-LE.B.5
7 lessons25 short videos6 key concepts, out loud
5.1
Slope as Rate of Change (Rise / Run)
Measure steepness as rise over run in real-world situations
F-IF.B.6
Key idea
Slope measures steepness as the vertical change (rise) divided by the horizontal change (run), representing a constant rate of change.
Learn to measure the steepness of a line by comparing vertical change to horizontal change and interpret what this rate means in real-world contexts.
Key concept · Lesson 5.1
Rise over run is a rate
Listen0:00 / 0:19
Transcript. Slope measures steepness as rise over run: how far the line climbs for each step to the right. Because that ratio never changes on a straight line, it is a rate, like kilometres per hour. A line falling from left to right has a negative slope.
5.2
The Slope Formula
Find the steepness of a line using any two points
8.EE.B.6
Key idea
The slope formula calculates the vertical change (rise) divided by the horizontal change (run) between any two coordinate points.
Learn how to use the slope formula to calculate a line's steepness directly from its coordinates without needing a graph.
Key concept · Lesson 5.2
Keep the subtraction order
Listen0:00 / 0:18
Transcript. The slope formula just measures rise over run using coordinates. Subtract the two y values on top and the two x values underneath, and start with the same point both times. Mixing the order flips the sign, which turns an uphill line into a downhill one.
5.3
Slope-Intercept Form (y = mx + b)
Graph lines and understand equations using slope and starting values
F-IF.C.7aF-LE.B.5
Key idea
In y = mx + b, 'm' is the slope (how steep the line is) and 'b' is the y-intercept (where the line starts on the vertical axis).
Learn how to use the slope and y-intercept to quickly graph any line and decode its real-world meaning.
Key concept · Lesson 5.3
Start at b, step by m
Listen0:00 / 0:20
Transcript. In this form the equation tells you how to draw the line. The value b is where it crosses the vertical axis, so plot that point first. Then m is the step: rise over run. An integer slope like three still means three up and one across.
5.4
Graphing with Intercepts (Cover-Up Method)
Find where a line crosses the axes to graph it quickly
F-IF.C.7a
Key idea
To find the x-intercept, set y to 0; to find the y-intercept, set x to 0. Plot these two points on the axes and draw a line through them.
Learn to find the x- and y-intercepts of a standard form equation and use them to graph the line.
Key concept · Lesson 5.4
Two intercepts make a line
Listen0:00 / 0:19
Transcript. Two points fix a line, and the easiest two are the intercepts. Set x to zero and solve for y to get the y-intercept. Set y to zero and solve for x to get the x-intercept. Plot both, draw through them, and keep any minus sign you uncover.
5.5
Horizontal & Vertical Lines
Graph flat and straight-up lines and find their slopes
F-IF.C.7a
Key idea
Horizontal lines have equations of the form y = k and a slope of zero, while vertical lines have equations of the form x = h and an undefined slope.
Learn how to graph horizontal and vertical lines, write their equations, and identify whether their slopes are zero or undefined.
Key concept · Lesson 5.5
Flat floor, standing wall
Listen0:00 / 0:21
Transcript. A horizontal line has the same output everywhere, so its equation is y equals a number and its slope is zero: a flat floor. A vertical line has the same input everywhere, so it is x equals a number, its slope is undefined, and it is not a function.
5.6
Direct Variation (y = kx)
Proportional relationships and lines that pass through the origin
8.EE.B.5
Key idea
Direct variation is a proportional relationship written as y = kx, where the graph is a straight line through the origin with a slope of k.
Learn to identify, write, and graph direct variation equations representing proportional relationships.
Key concept · Lesson 5.6
Direct variation: zero y-intercept
Listen0:00 / 0:21
Transcript. Direct variation is the simplest linear relationship: y equals k times x, with nothing added on the end. Its graph is a straight line through the origin. Find the constant by dividing an output by its input, and remember that a line with an intercept is not direct variation.
5.7
Review & Assessment
Graphing and interpreting linear functions
Review, practice, quiz and test
Key idea
Review graphing and interpretation of linear functions with targeted practice, a practice test, and a chapter test.
This is one chapter of the climb.
Algebra 1 spans 16 chapters, every lesson taught on video with a key concept you can hear, and Vector on hand to answer questions out loud.
