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Get Full AccessGraphing Linear Equations: Slope & yintercept (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 GoKarts, 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 xaxis and the second is the placement on the yaxis. The point is where the x and ycoordinates 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 xvariable. Since 3 is multiplied by x, 3 is the slope. The yintercept is a constant that is added in the equation. Since –10 is added, the yintercept is −10. Note that y=3x10 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 yintercept is a constant, so the yintercept is –10. This makes the equation y=2x10, 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 xaxis, and the vertical axis is the yaxis
 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 xaxis, and y is the distance from the origin on the yaxis.
 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].  yintercept DEFINE
The point where a line crosses the yaxis is called the yintercept. The yintercept is often represented as “b” in the slopeintercept form of a line.
 Slopeintercept 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

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