Graphing Linear Equations: Slope & y-intercept (y= mx + b)

Points 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.

The 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.