the ax+by+c=0 from of the line x=-5is ----------
Answers
Answer:
Horizontal and Vertical Lines
Vertical lines have equations of the form x = A , where A is a constant.
Horizontal lines have equations of the form Y = B , where B is a constant.
Examples
x = 2 this is the equation of a vertical line that passes through all points with x coordinate equal to 2.
y = 0 this is the equation of a horizontal line that passes through all points with y coordinate equal to 0 (x axis).
x = 0 this is the equation of a vertical line that passes through all points with x coordinate equal to 0 (y axis).
y = -3 this is the equation of a horizontal line that passes through all points with y coordinate equal to -3.
Interactive Tutorial Using Java Applet
Your browser is completely ignoring the <APPLET> tag!
Click on the button above "click here to start" and maximize the window obtained.
Use the sliders on the left control panel of the applet and set a = 1, b = 0 and
c = 2. You should have a vertical x = 2 (example above part a) that passes through all points with x coordinates equal to 2.
Set a = 0, b = 1 and c = 0, you should have a horizontal line y = 0 (example above part b) which is the x axis.
Set a = 1, b = 0 and c = 0, you should have a vertical line x = 0 (example above part c) which is the y axis.
Set a = 0, b = 1 and c = -3, you should have a horizontal line y = -3 (example above part d) that passes through all points with y coordinate equal to -3.
x and y Intercepts of the Graph of a Line
We now explore more general equations of lines with equations
ax + by = c, where a is not equal to zero and b is not equal to zero.
The x intercept is found by setting y = 0 in the above equation and solve for x.
ax + b(0) = c
x = c/a
Hence, the x intercept is at (c/a , 0).
The y intercept is found by setting x = 0 in the above equation and solve for x.
a(0) + by = c
y = c/b
Hence, the y intercept is at (0 , c/b).
Example Find the x and y intercepts of the graph of the equations given below.
2x - y = 2
4x + 2y = 0
Solution to the Questions in the Above Example
The x intercept is found by solving 2x = 2, which gives x = 1.
The x intercept is at (1 , 0).
Hence, the y intercept by solving -y = 2, which gives y = -2.
The y intercept is at (0 , -2).
The x intercept is found by solving - 4x = 0, which gives x = 0.
The x intercept is at (0 , 0).
Hence, the y intercept by solving 2y = 0, which gives y = 0.
The y intercept is at (0 , 0).
Interactive Tutorial Using Java Applet
Set parameters a = 2, b = -1 and c = 2 in the applet panel. This will define equation in the example above, part a. Locate the x and y intercepts and compare with the solution above.
Set parameters a = 4, b = 4 and c = 0. This will define equation in the example above, part b. Locate the x and y intercepts and compare with the solution above.
Set parameters b = 1 and c = 1. Change parameter a. Does the position of the x intercept change? Does the position of the y intercept change? Explain.
Set parameters a = 1 and c = 1. Change parameter b. Does the position of the x intercept change? Does the position of the y intercept change? Explain.
Let us write the equation ax + by = c in slope intercept form.
y = -(a/b)x + c/b
The slope is given by -(a/b). Set a, b and c to some values. Drag the red markers so that they are on the line, read their coordinates and find the slope of the line. Compare the slope found to -(a/b).
More References and Links
Slope Intercept Form Of a Line
Equations of Line Through Two Points And Parallel and Perpendicular.
Slope of a Line
Easy to use calculator to find slope and equation of a line through two points.Two Points Calculator
Another calculator to find slope, x and y intercepts given the equation of a line.Find Slope and Intercepts of a Line - Calculator
Find a Parallel Line Through a Point: Find a line that is parallel to another line and passes through a point.
Find a Perpendicular Line Through a Point: Find a line that is perpendicular to another line and passes through a point.
Match Linear Equations to Graphs
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Step-by-step explanation:
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