1. Date: Topic: Lines and Slope (1.2)
Definition of Slope
The slope of the line through the distinct points (x1, y1) and (x2, y2) is
where x2 – x1 = 0. y1 y2 y
Change in y
Change in x =
Rise
Run
y2 – y1
x2 – x1
(x1, y1) x1 x2
(x2, y2) x
Find the slope of the line with points (3, 2) and (-5, 5)

2. The Possibilities for a Line’s Slope
Positive Slope x y
m > 0
Line rises from left to right.
Zero Slope x y
m = 0
Line is horizontal.
Negative Slope x y
m < 0
Line falls from left to right.
m is undefined
Undefined Slope x y
Line is vertical.
m = 2

3. Slope-Intercept Form of the Equation of a nonvertical line with slope m and y-intercept b is y = mx + b
Find the slope and the y-intercept of the line whose equation is
2x – 3y + 6 = 0.
2x – 3y + 6 = 0
+ 3y y
To isolate the y-term, add 3y on both sides.
2x + 6 = 3y
3y = 2x + 6
Reverse the two sides. (This step is optional.)
Divide both sides by 3.
y = 2/3x + 2
The slope is 2/3.
The y-intercept is 2.

4. Graphing y=mx+b Using the Slope and Y-Intercept
Plot the y-intercept, b.
Plot a second point using the slope, m, rise over run.
Draw a line through the two points.
Graph the line whose equation is: -5 -4 -3 -2 -1 1 2 3 4 5
y = 2/3 x + 2
The slope is 2/3.
The y-intercept is 2.
We need two points in order to graph the line:
We can use the y-intercept, 2, to obtain the first point (0, 2).
We plot the second point on the line by starting at (0, 2), the first point. Then move 2 units up (the rise) and 3 units to the right (the run). This gives us a second point at (3, 4).

5. Point-Slope Form of the equation of a nonvertical line of slope m that passes through the point (x1, y1) is y – y1 = m(x – x1)
If given two points find the slope using the points,
and use one of the coordinates in the equation
Write the point-slope form of the equation of the line passing through (-1,3) with a slope of 4. Then solve the equation for y.
Solution We use the point-slope equation of a line with m = 4, x1= -1, and y1 = 3.
This is the point-slope form of the equation.
y – y1 = m(x – x1)
y – 3 = 4[x – (-1)]
Substitute the given values.
y – 3 = 4(x + 1)
We now have the point-slope form of the equation for the given line.
y – 3 = 4x + 4
We can solve the equation for y by applying the distributive property.
Add 3 to both sides.
y = 4x + 7

6. Equations of Lines Point-slope form: y – y1 = m(x – x1)
Slope-intercept form: y = mx + b
Horizontal line: y = b
Vertical line: x = a
General form: Ax + By + C = 0

7. Complete Student Checkpoint
Indicate whether each line
has a positive, negative,
zero, or undefined slope.
Write the equation of
the line in slope-intercept
form. (Assume scale is 1)
x-axis
y-axis
x-axis
y-axis a b c d
y-intercept 3
zero -3
undefined
positive
slope
-1/2 6
negative
equation:

8. Use the given conditions to write an equation in point-slope form and slope-intercept form.
Passing through (-3,2) and (3,6). Send you answer to me using the calculator

9. Slope and Parallel Lines If two nonvertical lines are parallel, then they have the same slope.
DAY 2
Write an equation of the line passing through (-3, 2) and parallel to the line whose equation is y = 2x + 1. Express the equation in point-slope form and y-intercept form.
y = 2x + 1 -5 -4 -3 -2 -1 1 2 3 4 5
(-3, 2)
Rise = 2
Run = 1
y – y1 = m(x – x1)
y1 = 2
m = 2
x1 = -3
Parallel lines have the same slope. Because the slope of the given line is 2, m = 2 for the new equation.
y – 2 = 2[x – (-3)]
y – 2 = 2(x + 3)
y – 2 = 2x + 6
Apply the distributive property.
y = 2x + 8
This is the slope-intercept form of the equation.

10. Slope and Perpendicular Lines
90°
Two lines that intersect at a right angle (90°) are said to be perpendicular. There is a relationship between the slopes of perpendicular lines.
Slope and Perpendicular Lines
If two nonvertical lines are perpendicular, then the product of their slopes is –1.
(2/3) • (-3/2) = -1
Slopes are negative reciprocals of each other
Find the slope of any line that is perpendicular to the line whose equation is 2x + 4y – 4 = 0.
4y = -2x + 4
y = -1/2x + 1
Slope is –1/2.
Any line perpendicular to this line has a slope that is the negative reciprocal, 2.

11. You Try Write an equation of the line passing through (-3,6) and
perpendicular to the line whose
equation is y=1/3 x +4
Express in point-slope form and
slope-intercept form.
Write an equation of the line
passing through (-2,5) and
parallel to the line whose
equation is y=3x+1. Express
in point-slope form and
slope-intercept form.
perpendicular slope:

12. Graphs and Viewing Windows
Bob purchased a house 8 years ago for $42,000. This year is was appraised at $67,500.
A linear equation V=mt + b, 0 ≤ t ≤ 15, represents the value V of the house for 15 years after it was purchased. Determine m and b.
Graph the equation and trace to estimate in how many years after the purchase of this house it will be worth $72,500
Write and solve an equation algebraically to determine how many years after purchase this house will be worth $74,000.