1. Slope is a number that indicates how steep the line is, and which direction the line points.
Lines that point down-hill have a negative slope.
Lines that point up-hill have a positive slope.
State whether the slope is positive or negative.
slope is positive
Line to the left: slope is positive. Line to the right: slope is negative.
slope is negative

2. Horizontal and vertical lines.
Horizontal lines are flat (no steepness). The slope is therefore zero (a number that indicates no steepness). Vertical lines are steep, so steep that the slope can not be defined. For vertical lines, we say the slope is undefined.
slope = 0
left: slope=0 right: slope is undefined
slope = undefined
Indicate which line has a slope of zero and which line has a slope so steep that it is undefined.

3. m stands for slope (think of mountain)
m = rise over run
run (tread)
rise = 7
run = 6
First identify if slope is negative or positive. This line has a positive slope. The rise = 7 and run = so rise/run = 7/6 so slope = 7/6 (or m = 7/6)
rise (riser)
m = 7/6
Find the rise, run, and slope of this line. Be sure to indicate if the slope is positive or negative.

4. b stands for y-intercept (think of bumps)
The y-intercept of a line is the number on the y axis where the line bumps into the y axis. It can be given as a point (such as (0, 3) or as the number on the y axis where the line bumps into the y axis.
Line to the left: b=3 and m=1 Line to the right: b=-4 and m=-4/3 (because slope is negative)
y intercept is (0, -4) or -4
y intercept is (0, 3) or 3

5. Give the y-intercept as a point and as a number for each line if possible. If it is not possible, explain why.
b = (0, 3) or 3
left: b=3 or b = (0, 3) right: no y intercept (never crosses y axis) so can not give a point or a number for b.
b = can not give b.
Line does not cross y axis and therefore does not have a y intercept.

6. Given the graph of a line:
You can find the slope (m)
You can find the y intercept (b)
m = 5/4 4
m = 5/ b = -1 5
b = -1

7. To write the equation of a line, all you need to know is the slope and the y-intercept of the line.
y = x +
Step 1: Write:
y = x +
Remember slope intercept form of a line: y = mx + b, where m is the slope, and b is the y-intercept.
Step 2: Fill in the first box with the number for slope.
slope
y-intercept
Step 3: Fill in the second box with the number for the y-intercept.
Equation of any line: y = mx + b

8. Find the equation of the line:
y-intercept = 2
y= x + 1 2 4
All we need to do is fill in the two boxes 4
rise/run = 4/4 which is 1 the slope is positive, so m = b = 2. Equation: y = 1x + 2 or y = x + 2.
m = 4/4 = 1
y = x + 2
Be careful to check and see if the slope is positive, or negative. This slope is positive.

9. Find the equation of the line:
y= x +
- 1 -2
y = -x - 2
slope is negative rise/run = 2/2 so slope is -1
m = - 2/2 = -1 2 2
Be careful to check and see if the slope is positive or negative. This slope is negative.
y-intercept = -2

10. Equations for horizontal and vertical lines
horizontal: y =3 vertical: x = -3
y = 0 x + 3
which reduces to:
y = 3
x = -3
This line has an undefined slope, and no y-intercept. But everywhere along the line, x = -3.

11. Find the equation of the line that passes through the two points: (2, 3) and (0, 5).
Step 1: Plot the points.
Step 2: Use a ruler and draw the line.
y = -x + 5
Step 3: Follow directions for finding the equation of a line (directions are on slide # 7)
y = -x + 5

12. Find the equation of the line that passes through the point ( -4, -4) and has a slope of -½.
y = - ½ x - 6
Step 1: Plot the given point.
Step 2: From the point, use the slope to find the next several points (rise 1 and run 2 remembering slope is negative.).
y = -1/2 x - 6
Step 3: Use a straight edge and draw the line.
Step 4: Find the equation.

13. Parallel lines have the same slope.
Find the equation of both lines.
Top red line: y = x Bottom green line: y = x – 5 Both lines have a slope of 1.
Top line: y = x + 5
Bottom line: y = x - 5

14. Find the equation of the line that is parallel to y = ¾ x + 3 and goes through the point ( 0, -3).
Step 1: Realize that y = ¾ x + 3 is in the y = mx + b form. Therefore, the slope of y = ¾ x + 3 is ¾.
y = ¾ x - 3
y = 3/4x - 3
Step 2: Plot (0, -3). We know our line goes through this point.
Step 3: We also know that our line is // to y = ¾ x + 3, so it must have the same slope. So the slope of our line is also ¾ .

15. Find the y intercept of the line: 5x + 2y = 10
2.5 2 5
b = 5 The easier way would be to realize that every y intercept is an (x, y) point where x = 0, so the only point you need to plug in for x would be 0. When x=0, y=5.
Now what? The line is not in y =mx + b form. No worries. Just plug in some numbers for x and solve for y. Then you will have (x, y) points to plot. After you plot the points and draw the line, you can see where it bumps into the y axis. (There is an easier way- can you think of it?)
y-intercept is 5 (b=5)

16. Given that x and y have a linear relationship, find the value of a.
If x and y have a linear relationship, then when you plot the points, it will make a line. x y 3 1 5 -1 -2 -4 a
Plotting the points and drawing the line shows that when x = -4, y = Therefore, a = -5
When x is -4, y is -5.
Therefore, a in the table is -5.