This document discusses slopes and equations of lines. It defines slope as the rate of change of a straight line and provides the slope formula. Positive slopes mean the graph lines go up from left to right, while negative slopes mean lines go down. There are three common forms for writing linear equations: slope-intercept form where the slope is the coefficient of x; standard form where A, B, and C don't represent slope or y-intercept; and point-slope form used when a point and slope on the line are known. Special cases for horizontal and vertical lines are also covered. Videos demonstrate calculating slope and writing equations in slope-intercept and point-slope form.
2. SLOPE
Slope is the rate of change of a straight line (linear)
graph/function.
What are some of the things we have learned about slope so far?
Can you come up with an equation to calculate slope?
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3. SLOPE CONT.
Positive slopes mean the graph is going up from left to
right
Negative slopes mean the graph is going down from left
to right
The steeper the line the bigger the slope (rate of change)
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4. HOW TO CALCULATE SLOPE…
To calculate a slope from a graph or two
coordinate points we use the formula:
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5. FINDING SLOPE
• Use the slope formula to find the slope of the
given examples.
1. (-2, 5) and (4, 12)
2.
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7. LINEAR FUNCTIONS
Linear Functions are functions whose
graphs are straight lines. They are
straight because their rate (slope) is
constant. There are 3 forms of a linear
function.
• Slope-Intercept Form
• Standard Form
• Point-Slope Form
8. SLOPE-INTERCEPT FORM
It is slope-intercept form because the y (or dependent variable) is by
itself and the highest exponent of x (or independent variable) is 1.
The slope is always the value with the x in THIS FORM. It could be
written y = b + mx.
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9. EXAMPLES
Write the equation of the line in slope-intercept form.
1.
2.
3. m= 1/5
b = -2
4. y-intercept = 200
slope = -23.724
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10. SPECIAL CASES
Horizontal Lines have a slope of 0. Therefore, we cannot
write a slope-intercept equation for them.
Horizontal lines intersect the y-axis.
Therefore, the equation for a horizontal line just states
what that y-value is.
Vertical lines have an undefined slope. Therefore, we
cannot write a slope-intercept equation for them, either.
• Instead, we notice that the coordinate points of a
vertical all have the same x-value.
• So, the equation for a vertical line just states what that
x-value is.
12. LINEAR STANDARD FORM
This is another form for writing a linear
function.
It is used to represent situations where two
variables are changing at a constant rate.
In this form, the A, B, and C do not
represent the y-intercept or the slope of the
graph.
It is also important to understand that in
many cases standard form is only written
using integers (+/- whole numbers) for A, B,
and C.
It is possible for A, B, and C to be zero but it
cannot be both A and B.
13. WHICH EQUATIONS ARE IN LINEAR STANDARD FORM?
Linear Standard
Form
-2x – 4y = 9
X=2
Y=1
Not Linear Standard
Form
1/3x – 7y = 12
y = -1/2x + 3
y – 4 = 2(x + 5)
8 = 2.5x – 3y
10 = -3xy
4x + 3y = 20
