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Graphing Linear Equations: Slope & y-intercept (y= mx + b)
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What you will learn from this videoWhat you will learn
- We'll learn how to graph an equation in the form y = mx + b.
- We will also learn how to find the equation of a line on a coordinate plane.
- And we'll see how this knowledge can help us ride Go-Karts, visit a theme park and go skiing!
- Discussion Questions
Before Video
How do you graph a point on a coordinate plane?ANSWERPoints are given using ordered pairs (x, y) so the first number is the placement on the x-axis and the second is the placement on the y-axis. The point is where the x- and y-coordinates meet.
A relation is a rule that relates two variables. We often represent relations with graphs, tables of values, and equations.
A rate is a ratio between two measurements with different units, like km/h or dollars/lb.
A constant is a value that is fixed and doesn’t change, like the height of an adult, the cost to book a taxi, or the base fee to hold a special event in a venue.
The line would be steep, because that is how you show something moving a large distance in a short time.
After Video
What is slope?ANSWERThe slope is the [ggfrac]rise/run[/ggfrac]. It is a rate that relates the two variables on a coordinate plane.
A linear relation with a positive slope shows that as one variable increases the other also increases. This is the opposite of a negative slope, whereas one variable increases, the other decreases.
The slope is a rate, so is multiplied by the x-variable. Since 3 is multiplied by x, 3 is the slope. The y-intercept is a constant that is added in the equation. Since –10 is added, the y-intercept is −10. Note that y=3x-10 is the same as y=3x+(-10).
The rate is the amount she sells each glass for, written as $2/glass. The constant is the cost of making the lemonade. Since the cost is something Molly needs to spend, it is negative. So, the constant is –$10.
The slope is a rate, so the slope is $2/glass. The y-intercept is a constant, so the y-intercept is –10. This makes the equation y=2x-10, where x represents the number of glasses sold and y represents the amount of profit. I would label the horizontal axis “Number of glasses sold” and the vertical axis “Profit.” This is because Molly uses the number of glasses sold to calculate her profit. The number of glasses sold is the independent variable, and the profit is the dependant variable.
- Vocabulary
- Coordinate plane DEFINE
Two number lines that intersect at 0 and are perpendicular to each other, where the horizontal axis is the x-axis, and the vertical axis is the y-axis
- Origin DEFINE
The point where the two number lines cross on a coordinate plane: (0, 0).
- Ordered pair DEFINE
Describes the position of a point on a coordinate plane. An ordered pair is written (x, y) where x is the distance from the origin on the x-axis, and y is the distance from the origin on the y-axis.
- Slope DEFINE
A rate that describes how y changes in relation to x.
slope = [ggfrac]rise/run[/ggfrac] = [ggfrac]change in y/change in x[/ggfrac] = [ggfrac]( y₂ - y₁ )/( x₂ - x₁ )[/ggfrac]. - y-intercept DEFINE
The point where a line crosses the y-axis is called the y-intercept. The y-intercept is often represented as “b” in the slope-intercept form of a line.
- Slope-intercept form of a line DEFINE
The equation of a linear relation written in the form y=mx+b.
- Table of values DEFINE
A table with two columns, with the left column labeled “x” and the right column labeled “y.” Each row in a table of values represents an ordered pair.
- Coordinate plane DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide