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4.2 Determining Slope and Y-intercept
8.4.C - Use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical
and real-world problems.
8.5.B - Represent linear non-proportional situations with tables, graphs, and equations in the form of y=mx+b,
where b  0.
8.1.A - Apply mathematics to problems arising in everyday life, society, and the workplace.
Equations
Knowing how to find the slope and the y-intercept helps us to graph a line when we know its equation, and also
helps us to find the equation of a line when we have its graph. The equation of a line can always be written.
Every straight line or ____________ relationship can be represented by an equation: y = mx + b which is called
________________________. Remember a linear relationship has a _______________________of
change.
The __________“m” of this line - its steepness, or slant - can be calculated like this:
m or slope = change in y-value
change in x-value
and “b” is the ______________________.
The y-intercept of this line is the value of y at the point where
the line crosses the y-axis.
Slope
We're familiar with the word "slope" as it relates to mountains. Skiers and snowboarders refer to "hitting the
slopes." On the coordinate plane, the steepness, or slant, of a line is called the slope. Slope is the ratio of the
change in the y-value over the change in the x-value. Carpenters and builders call this ratio the "rise over the run."
Using any two points on a line, you can calculate slope using this formula.
Let's use these two points to calculate the slope m of this line.
A = (1,1) and B = (2,3)
4.2 Determining Slope and Y-intercept
Y-Intercept
There's another important value associated with graphing a line on the coordinate plane. It's called the
"y intercept" and it's the y value of the point where the line intersects or _____________ the y- axis.
You can find the y-intercept by looking at the graph and seeing which point crosses the y axis. This
point will always have an x coordinate of zero.
What is the y-intercept and slope of this graph?
X
Y
0
1
2
7
4
13
6
19
8
25
We use the same information for tables.
Initial Value
To find the initial value, we need to find what the output (y) is when the input (x) is zero. We can either
extend the table backwards following the pattern or solve the equation.
What is the rate of change? Find the initial value.
X
Y
5
16
10
14
15
12
20
10
A phone salesperson is paid a minimum weekly salary and a commission for each phone sold, as shown
in the table. Confirm that the relationship is linear and give the constant rate of change and the initial
value.
Number of
Weekly
Phones
Income ($)
Sold
10
$480
20
$630
30
$780
40
$930
4.2 Determining Slope and Y-intercept