Pre-Calculus
Chapter One
Day 2
Goals:
 Calculate slope
 Know how slope relates to the graph. What is the slope of a horizontal
line? Vertical line? What does a positive slope look like?
 Find linear equations for given lines
 Calculate the midpoint of a segment
NOTES:
Formula for calculating slope:
It doesn’t matter how you assign the labels of (x1, y1) and (x2, y2), BUT you
must be CONSISITENT.
Use your calculator program to CHECK YOUR WORK. The formula has other
applications, so you must also learn the formula.
Remember these facts:
1. Oblique lines have a positive or negative slope.
2. Horizontal lines have a slope of zero.
3. Vertical lines have an undefined slope because division by zero is not
defined.
Writing linear equations:
Slope-intercept form:
Point-slope form:
Standard form:
You also need to know these facts about parallel and perpendicular lines:
1. Parallel lines have the same (equal) slopes.
2. Perpendicular lines have slopes that are opposite reciprocals.
Formula for midpoint of line segment:
Examples:
Determine the slopes and y-intercepts of the lines defined by the following equations.
1. 2x – 8y = 15
3.
𝑥−𝑦
4
+3=5
2. 8y = 15
𝑥
4. 4y – 3 = 5
5. 7x = -15
6. Sketch a graph of 2y + 5x – 8 = 0
7. Find the equation of the line that passes through (2, -4) with slope of ½.
8. Find the equation of the line in STANDARD FORM of the line that passes through the
points with the given slopes.
a) Point (3, -1) with slope = 10
b) Point (-1, 3) with m = 0
c) Point (4, -5) with an undefined slope
d) Passes through the points (1, 3) and (-2, 3)
e) Passes through the points (-9, 2) and (1, 5)
f)
Passes through the points (8, -10) and (8, 0)
9. Find the equation of the line in slope-intercept form of the line parallel to 3x + 4y = 5 that passes through the point (3, 1).
10. Find the equation of the line in standard form of the line perpendicular to 3x + 4y = 5 that passes through the point (3, 1).
11. If (5, -6) and (3, -10) are endpoints of a line segment, find the midpoint.
12. If (4, 4) is the endpoint of a line segment and (2, 1) is the midpoint, find the other
endpoint.
13. If (5, -6) is the endpoint of a line segment and (3, -1) is the midpoint, find the other
endpoint.
ASSIGNMENT:
Determine the slope of the lines passing through these points:
1. (3, -1) and (-7, -1)
2. (3, -5)(3, 2)
3. (7, 4) and (-6, 13)
Determine the slope of the lines defined by the following equations:
3. 2x + 8y = 11
4. 7x = 2
5.
𝑥+2
3
+ 2(1 − 𝑦) = −2𝑥
6. Find the equation of the line through (0, -3) with m = 3/4
7. Find the equation of the line through (-1, -3) with m = 3/2
8. Find the equation of the line in STANDARD form of the line through (5, 11) with m = -2.
9. Find the equation in STANDARD form of the line through (2, -2) and (2, 17).
10. Find the equation of the line in slope –intercept form of the line through (-2, 8) and (5,
6).
11. Find the equation of the line parallel to 6x + 2y = 19 and passes through (6, 13).
12. Perpendicular to 6x + 2y = 19 and passes through (-6, -13).
13. Find the midpoint of a line segment whose endpoints are (5, -6) and (12, 7).
14. Find the other endpoint of a line segment with midpoint of (-4, -10) and endpoint of (12, -6).