Determining Slopes of Lines From Two Points and Equations of

Sometimes you need to find the slope of a line based on two given points. Sometimes you need to read a linear equation and determine the slope of a lone from the equation. This solution covers both of these cases and shows how to avoid errors, especially when determining the slope from two points. It also shows how to interpret information from all three forms of the equation of a line.

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Finding The Slope of a Line From Two Points

Given two points on a coordinate system that are described as the ordered pairs of (x1,y1) and (x2,y2), you may find the slope(m) of the line from the following equation.

m=(y2-y1)/(x2-x1)

Beginners using this formula typically ask "Which ordered pair describes "Point 1" and which describes "Point 2". IT DOESN'T MATTER! But once you make the decision on which ordered pair you will assign to "Point 1" and "Point 2", you must be consistent
in your ...

Solution Summary

This solution shows how to determine the slope of a line either from two given coordinate points or from an existing linear equation.

1.For the pairs of lines defined by the following equations indicate with an "I" if they are identical, a "P" if they are distinct but parallel, an "N" (for "normal") if they are perpendicular, and a "G" (for "general") if they are neither parallel nor perpendicular.
3x + 4y + 5 = 0 and y = - 3
4 x - 54 .
x = 2 and y = p

The fully-formattted image is attatched from a scanned document. Please explain, where possible.
Three points 4(2,3), B(-1, -2) and C(-1,6) and the circle that. passes through them.
(a) (i) Find the slope of the line that passes through A and B.
(ii) Find the coordinates of the midpoint of the line segment AB.
(iii) Find t

Please see the attached file for complete description
1. Solve the system by graphing.
x + y = 4
-x + y = 2
2. Determine which twoequations represent perpendicular lines.
3. Solve the system by graphing.
3x + y = 6
3x - y = 0
4. Graph the inequality y < -3
5. Solve the following system of linear inequalit

1. Why is it true that any twopoints satisfying a linear equation will give you the same graph for the line represented by the equation?
2. How do you interpret the slope and y intercept in a real world case?
3. By looking at two linear equations, how can you tell that the corresponding lines are pa

Explore the following function. You are to decide which of threee lines given are tangent to the graph of f(x) at given points.
The function to define is
F(x)=2x^3-4x^2+3x-5
The possible tangent lines are:
y= x-5
y= 2x-5
y= 3x-5
a) what is/are the zero(es) for this function? In other words, what is the solu

Please see the attached file for the fully formatted problems.
Write the equation of the line with given slope and y-intercept. Then graph each line using
the slope and y-intercept
1. Slope: -2; y-intercept: (0, 4)
2. Slope: 5; y-intercept: (0, -2)
3. Slope: ; y-intercept: (0, 8)
4. Find the slope of any line pe

Please help me with these problems and please show all work and steps to your solutions. This will help me better understand the problems once I have the answer and the steps for it. Thanks!
Please show work
1. How do we write the equation of a horizontal line? What would be an example?
2. How do we write the equation of

Given three points, there is one line that can be drawn through them if the points are colinear. If the three points are noncolinear,there are three lines that can be drawn through pairs of points. For three points, three is the greatest number of lines that can be drawn through pairs of points. Determine the greatest number of