Transcript Section 2.3 – Linear Functions and Slope

Section 2.3 – Linear Functions and
Slope-Intercept Form
Consider a nonvertical line in the coordinate
plane. If you move from any point on the line to
any other point on the line, the ratio of the
vertical change to the horizontal change is
constant.
That constant ratio is the slope of the line.
Section 2.3 – Linear Functions and
Slope-Intercept Form
The slope of a nonvertical line is the ratio of the
vertical change to the horizontal change
between two points.
You can calculate the slope by finding the ratio of
the difference in the y-coordinates to the
difference in the x-coordinates for any two points
on the line.
Section 2.3 – Linear Functions and
Slope-Intercept Form
Section 2.3 – Linear Functions and
Slope-Intercept Form
Problem 1:
What is the slope of the line that passes
through the given points?
a. (-3, 7) and (-2, 4)
b. (3, 1) and (-4, 1)
c. (7, -3) and (7, 1)
d. (5, 4) and (8, 1)
e. (2, 2) and (-2, -2)
f. (9, 3) and (9, -4)
Section 2.3 – Linear Functions and
Slope-Intercept Form
Problem 1:
Use the slope formula to show that it does not
matter which point you choose for (x1, y1).
Section 2.3 – Linear Functions and
Slope-Intercept Form
Section 2.3 – Linear Functions and
Slope-Intercept Form
A function whose graph is a line is a linear
function. You can 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.
Section 2.3 – Linear Functions and
Slope-Intercept Form
A special form of a linear equation is called
slope-intercept form.
An intercept of a 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.
Section 2.3 – Linear Functions and
Slope-Intercept Form
Section 2.3 – Linear Functions and
Slope-Intercept Form
Problem 2:
What is an equation of each line?
a. m = 1/5 and the y-intercept is (0, 3)
b. m = 6 and the y-intercept is (0, 5)
c.
d.
Section 2.3 – Linear Functions and
Slope-Intercept Form
Problem 4:
What is the graph of -2x + y = 1?
Problem 4:
What is the graph of 4x – 7y = 14?
Section 2.3 – Linear Functions and
Slope-Intercept Form
Problem 3:
Write the equation in slope-intercept form. What
are the slope and y-intercept?
a. 5x – 4y = 16
b. -3/4x+1/2y = -1
c. 3x + 2y = 18
d. -7x – 5y = 35
Section 2.3 – Linear Functions and
Slope-Intercept Form
Lesson Check
Section 2.3 – Linear Functions and
Slope-Intercept Form
Lesson Check