Today’s Lesson:
What:
Why:
. . . so I can use slope-intercept form in order to graph
equations.
How:
. . . by taking accurate notes, participating in ALL practice
activities, and completing my homework.
Just plug in
the “x” values!
What is the slope-intercept
formula, including what
“m” stands for and what
“b” stands for?
Remember . . .
A linear equation is an equation with 2 different variables
(like y = 4x + 1 )– with no exponents. Also, they graph as a
___________________
line!
straight
Well, when a linear equation is written in a specific
order/ format, we call it slope-intercept form . . .
In other words, when the equation is written like this:
y = 5x + 2
Y is isolated on
one side, and the
x term comes
before the
constant!
The slope-intercept formula is: y= mx + b
What is y = mx + b ??
Well, the
intercept.
stands for ____________,
slope
& the
stands for the y-
steep
slope – measure of how ______________
a line is. It is often described as a ratio
𝑟𝑖𝑠𝑒 (𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒)
of a line’s rise over its run –(
).
𝑟𝑢𝑛 (ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒)
y axis
y-intercept– point where the line crosses the ____________________
.
Consider the
diagram . . .
“Slope” Video Break . . .
Let’s apply it . . .
1)
y = 3x + 2
Step 1:
Identify the “m” and the “b” :
𝟑
m = 3 or
𝟏
b=2
Step 2: Plot the y-intercept or b
Step 3: Apply slope--rise 3 and run 1 . . .
Positive slopes
will always
graph as
UPHILL lines!
y = mx + b
2)
y = -4x + 6
y = mx + b
m = -4
b= 6
Negative slopes will
always graph as
DOWNHILL lines!
When the slope is
negative, we FALL
instead of RISE . . .
3)
y=
𝟏
x
𝟐
m=
-3
𝟏
𝟐
b = -3
y = mx + b
Video Break (let’s review what we’ve learned so far) . . .
What if we have the graph Only??
We can easily use “y = mx + b” to come up with the equation as well!
How?
y-intercept (where it crosses the y axis).
Study the graph of the line. Identify the _________________
This is the “b.”
Then, determine the slope. Is it an uphill or a downhill? This tells you whether the
slope is positive or ______________.
Count the “rise” grid moves versus the “run” grid
negative
moves. This is the “m.”
4) m = -
𝟑
𝟒
b = -2
So, the equation is . . .
𝟑
y = - 𝟒 x + (-2)
________________
Downhill means
negative slope!
5)
Uphill means
positive slope!
y = mx + b
m=
𝟐
𝟏
b= 2
y = 2x + 2
So, the equation is . . . ________________
6)
Downhill means
negative slope!
y = mx + b
m= -
𝟏
𝟓
b = -3
𝟏
y = - 𝟓 x + (-3)
So, the equation is . . .________________
Wrap it up/Summary:
1) Write the slope-intercept formula and explain
what “m” stands for and what “b” stands for.
y = mx + b
“m” stands for the slope and “b” stands for the y-intercept.
homework
Finish worksheet (front and back).
END OF LESSON