1. 1.2 Slopes and Intercepts equation for a given line in the coordinate
Objectives: Graph a linear equation. Write a linear
equation for a given line in the coordinate
plane.
Standards: K Apply an appropriate technique to graph
a linear function.
L Write the equation of a line when
given the graph of the line.

2. Y = 3x - 2 m = 3, b = -2 Y = 1/2x + 3/4 m = ½, b = ¾ m = 0, b = 5
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
Y = 1/2x + 3/4
m = ½, b = ¾
Y = 5
m = 0, b = 5
Y = -2x
m = -2, b = 0

3. II. Identify the slope, m, and y-intercept, b, for each line
II. Identify the slope, m, and y-intercept, b, for each line. Then graph.
Positive slope goes up to the right & negative slope goes up to the left.
x + y = 6 *
m = _______
b = _______
y = x + 3 *
m = _______
b = _______

4. II. Identify the slope, m, and y-intercept, b, for each line
II. Identify the slope, m, and y-intercept, b, for each line. Then graph.
3x + 6y = 18 *
m = ________
b = ________

5. 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)

6. 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)

7. 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.

8. IV. Find the x and y intercepts.
4x + y = -4
X Intercept
4x + 0 = -4
4x = -4
x = -1
(-1,0)
Y Intercept
4(0) + y = -4
y = -4
(0, -4)
x + 3y = 12
X Intercept
x + 3(0) = 12
x = 12
(12,0)
Y Intercept
0 + 3y = 12
3y = 12
y = 4
(0,4)

9. IV. Find the x and y intercepts.
x + ½ y = -2 *
X Intercept
Y Intercept

10. 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
Horizontal Line Zero Slope
Y = 9

11. VI. Write an equation in slope intercept form for each line.
Ex 1. A line passing through ( 2, 4) with a slope of ½.
4 = ½ (2) + B
4 = 1 + B
3 = B
Y = ½ x + 3
Ex 2. A line with a slope of zero passing through (-2, -6).
Zero slope means it’s a horizontal line so y = #
Y = -6

12. VI. Write an equation in slope intercept form for each line.
Ex 3. A line passing through (0, -1) and (2,2).
Find the slope. M = 3/2
Plug slope and 1 of the above points into y = mx + b.
-1 = 3/2(0) + B
-1 = B
Y = 3/2x -1

13. 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.

14. 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.

15. 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.