Linear Equations

1. Mr. Gamboa

2. •A line is a geometric
object that is always
straight, has no ends,
and is infinitely thin
•A line can be modeled
by an equation
•A line is named by two
specific points that are
on it
• This line would be
named “Line AB”

3.  This form gets its name for having the slope
and y-intercept as part of the equation
 Slope-Intercept Form has the format:
y= mx + b
 This line equation form is easy for pulling
important graph information from
slope y-intercept

4.  Represented by “m” in slope-intercept form
 Describes the direction of the line
 Positive Slope = Line rises from left to right
 Negative Slope = Line falls from left to right
 Vertical Line = Infinite slope
 Horizontal Line = Zero Slope
 Shows how much a line rises relative to how
much it advances left to right
 Can be found by solving:
y2 – y1
x2 – x1
m=
For points (x1 , y1)
and (x2 , y2)

5.  Points on a line where the line crosses the y-
axis or the x-axis
 The point that crosses the
y-axis is the y-intercept
 Shown by Point Y
 (0, Y)
 The point that crosses the
x-axis is the x-intercept
 Shown by Point X
 (X, 0)

6.  What kinds of slopes do we see on this clock?

7.  The slope can be thought of as a rate – how
much one object changes in relation to
another object
 In our slopes, we find out how much the y-
direction (up or down) changes in relation to
the x-direction (left or right)
 In rates we use objects (pages, legs, hot
dogs, etc.) and units (feet, miles, liters,
minutes, etc.)
 We usually use the word “per”
 Ex) I can eat 5 hot dogs per hour

8.  If our rate is increasing in quantity, our rate
will be positive
 Ex) A plate of food has a temperature of 50° and
while cooking it in a microwave, it increases by
5° every 10 seconds.
 If our rate is decreasing in quantity, our rate
will be negative
 Ex) A plate of food has a temperature of 100°
and is decreasing by 5° per minute.

9.  What are some rates that we hear when
talking about cars?

10.  Amount of an item that a problem starts with
 We can have Initial Quantities of anything!
 Initial quantities are either added to,
subtracted from, or stay the same
 https://youtu.be/tHq1vg2B6iA

11.  How can our slope-intercept equation
represent Rates and Initial Quantities?
Y = mx + b
??? ???

12.  A SnapChat user has shared 3 SnapChats with
her friends today. Since she is on vacation,
she continues to send 5 SnapChats per day
for 5 more days. Find the equation that
represents this situation. Then graph the
equation.
y = 5x + 3