View
214
Download
0
Category
Preview:
Citation preview
1.2 Slopes and InterceptsObjectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane.
Standards: 2.8.11.K Apply an appropriate technique to graph a linear function. 2.8.11.L Write the equation of a line when given the graph of the line.
I. Write the equation in slope-intercept form for the line that has the indicated slope, m, and y-intercept, b.
m = 3, b = -2 y = 3x - 2
m = ½, b = ¾ y = 1/2x + 3/4
m = 0, b = 5 y = 5
m = -2, b = 0 y = -2x
II. Identify the slope, m, and y-intercept, b, for each line.
Then graph. Positive slope goes up to the right & negative
slope goes down to the right.
y = x + 3 *m = _______b = _______
x + y = 6 *m = _______b = _______
II. Identify the slope, m, and y-intercept, b, for each line. Then graph.
3x + 6y = 18 *
m = ________
b = ________
III. Find the slope of a line if you know the coordinates of two points on the line.
In a graph, the slope of a line is the change in vertical units divided by the corresponding change in the horizontal units.
m = Change in y = Rise = y2 – y1
Change in x Run x2 – x1
(0, 4) and (3, 1)
m = Change in y = Rise = y2 – y1
Change in x Run x2 – x1
(1, -3) and (3, -5)
(3, -2) and (4, 5)
(-10, -4) and (-3, -3)
IV. Find the x and y intercepts.
The x intercept of a graph is the x-coordinate of the point where the graph crosses the x-axis. In order to find the x intercept (x, 0), substitute zero for y in an equation for the line and solve for x.
The y intercept of a graph is the y-coordinate of the point where the graph crosses the y-axis. In order to find the y intercept (0, y), substitute zero for x in an equation for the line and solve for y.
IV. Find the x and y intercepts.
4x + y = -4
x-intercept
y-intercept
x + ½ y = -2
x-intercept
y-intercept
IV. Find the x and y intercepts.
1. x + 3y = 12 2. -3x + y = -9
3. x – y = -1 4. 5x – 8y = 16
5. 7x + 3y = 2 6. -x + 8y = -6
V. Vertical Lines vs. Horizontal Lines
A horizontal line is a line that has a slope of zero.y = # is a horizontal line.
A vertical line is a line that has an undefined slope.x = # is a vertical line.
x = -2 Vertical Line Undefined Slope
y = 2 Horizontal Line Zero Slope
y = 9 Horizontal Line Zero Slope
VI. Write an equation in slope intercept form for each line.
Ex 1. A line passing through (2, 4) with a slope of ½.
Ex 2. A line with a slope of zero passing through (-2, -6).
Zero slope means it’s a horizontal line so y = #
VI. Write an equation in slope intercept form for each line.
Ex 3. A line passing through (0, -1) and (2,2).
Writing Activities: Slopes and Intercepts
1a). In your own words, define the slope of
a line.
1b). Give an example of three lines with the
same slope.
Writing Activities: Slopes and Intercepts
2a). In your own words, define the y-intercept of a line.
2b). Give an example of three lines with the
same y-intercept.
Writing Activities: Slopes and Intercepts
3). What are the characteristics of a line that
has the equation y = mx?
4). What does the slope of a line indicate
about the line? Include some examples.
5). Explain the difference between a line
with a slope of 0 and a line with no
slope.
Homework
Integrated Algebra II- Section 1.2 Level A
Honors Algebra II- Section 1.2 Level B
Recommended