Download Lesson 2_3

Lesson 2.3 Summary
Objective: To graph linear equations.
To write equations of lines.
MA.912.A.3.10, MA.912.A.2.6
Importance:
The slope represents the rate of change between two quantities. Many real-life
applications are model using slope.
The slope of a nonvertical line is the ratio of the vertical change to the horizontal
change between two points. You can calculate slope by finding the ratio of the
difference in the y-coordinate to the difference in the x-coordinate for any two
points on the line.
Slope =
𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒 (𝑟𝑖𝑠𝑒)
ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒 (𝑟𝑢𝑛)
=
𝑦2− 𝑦1
𝑥2 − 𝑥1
, where 𝑥2 - 𝑥1 ≠ 0
You can choose either point for (𝑥1 ,𝑦1 )
Positive slope – means line rises from left to right
Negative slope – means line falls from left to right
Zero slope – means line is horizontal
Undefined slope – means line is vertical
A function whose graph is a line is a linear function. You represent a linear
function with a linear equation, such as y = 6x - 4. A solution of a linear equation
is any ordered pair (x, y) that makes the equation true.
An intercept of line is a point where a line crosses an axis. The y-intercept of a
nonvertical line is the point at which the line crosses the y-axis. The x-intercept of
a nonhorizontal line is the point at which the line crosses the x-axis.
The slope-intercept form of an equation of a line is y = mx + b, where m is the
slope of the line and (0, b) is the y-intercept.
From a line graph, you need the y-intercept (the point where the line crosses the
y-axis) and another point on the line to find the slope.
You can rewrite a linear equation in slope-intercept form by solving for y. You
can clear fractions from an equation by multiplying all terms on both sides of the
equation by the least common denominator. The least common denominator is
the smallest common multiple of all the denominators that is therefore divisible
by each of the denominators.
Steps to graph a linear equation:
1. Write the equation in slope-intercept form by solving for y in terms of x.
2. Plot the y-intercept, which is the point where the line crosses the y-axis.
The y-coordinate of this point is the constant term following the x term in
the equation.
3. Use the slope to find a second point on the line. From the y-intercept
point, move x units to the right or left (depending on whether the slope is
positive or negative) and y units up or down (again, depending on whether
the slope is positive or negative) to plot the second point.
4. Draw a line through the two points.
Examples:
1. What is the slope of the line that passes through the given points?
a. (5, 4) and (8, 1)
b. (2, 2) and (-2, -2)
c. (9, 3) and (9, -4)
d. Use the slope formula to show in part (a) that it does not matter which
point you choose for (𝑥1 , 𝑦1 ).
2. What is an equation of each line?
a. m = 6, y-intercept is (0, 5)
b.
c. Using the graph from part (b), do you get a different equation if you use
(-6, 0) and the y-intercept to find the slope of the line? Explain.
3. Write the equation in slope-intercept form. What are the slope and yintercept?
a. 3x + 2y = 18
b. -7x -5y = 35
4. What is the graph of 4x – 7y = 14?
Homework: pgs. 78-80 ex: 14, 19, 26, 33, 43, 48, 49, 56, 62b only, 63