Download Section 1-2: Graphs and Lines

1-2: Graphs and Lines
Objectives:
1. Slopes
2. Graph line equations
3. x- and y-intercepts
4. Find the equation of a line in 3 forms
5. Vertical and horizontal lines
How to find slope of a line:
EX: Find the slope of the line passing through the
given two points:
a. (-2, 7) and (-3, -1)
b. (8, 2) and (3, 4)
Note: If m > 0 (slope is positive), the line rises from
left to right;
If m < 0 (slope is negative), the line falls from left to
right;
Definition: A linear equation in two variables is an
equation that can be written in the standard form:
Note: No fractions in standard form!
Ex:
How many points are needed to graph a line
equation?
It’s easy to use two special points:
Using intercepts to graph
• x-intercept: the point where the graph intersects
the x-axis. To find x-intercepts, let = 0 and
solve for . Always express as an ordered pair
(x, 0)
• y-intercept: the point where the graph intersects
the y-axis. To find y-intercepts, let = 0 and
solve for . Always express as an ordered pair
(0, y)
Ex graph 2x – 3y = 6.
Ex: graph 4x + 2y = 0
Note:The x- and y-intercept is the same point –
which is not enough to graph a line. You need
another point! Pick any x-value & plug it in & solve
for y.
Three forms of a line:
1. Point-slope form:
Advantage: works with any point, not just yintercept.
2. Slope-intercept form:
3. Standard form: Ax + By = C
(A, B, C are integers)
Ex: a) Write an equation of a line w/slope
-3/7 and y-intc (0, 2)
b) Write an equation of a line passing through (-2, 1)
and (0, 5)
Note: An equation in standard form can easily be put
into slope-intercept form by simply solving for y.
Ex:
Ex: Write an equation of a line w/slope -1/2 going
through (3, -2). Give all three forms.
Ex: Find the standard form and slope-intercept form
of the equation of the line that passes through the
points (3, -2) and (7, 4)
Special lines:
Vertical line:
Horizontal Line:
Ex (vertical/horizontal lines) Write the equation of
the vertical and horizontal lines through the point (6,
-5).
Ex (Finding information about a line with graph
given)
Use the graph of each line to find x-intercept, yintercept, and slope. Write the slope-intercept form
of the equation of the line.
Applications
Ex The management of a company that
manufactures skateboards has fixed cost (cost at 0
output) of $300 per day and total cost of $4,300 per
day at an output of 100 skateboards per day. Assume
that cost C is linearly related to output x.
A)
Find an equation of the line relating output
to cost. Write the final answer in the form C =
mx + b;
B) Graph the cost equation from part A) for
0 ≤ x ≤ 200 .
Practice Problems:
1. Find the slope of the line represented
by the equation
3x – 2y = 6
2. Write the equation of the line that
passes through points with coordinates
(4, 2) and (-2, -6). Write this equation in
point slope form, slope intercept form
and standard form.
Answers to practice problems:
1. 3/2
2. y – 2 = 4/3(x - 4), y = 4/3x – 10/3, 4x – 3y = 10