Math, asked by ayeshasiddiqua17026, 1 month ago

the ax+by+c=0 from of the line x=-5is ----------

Answers

Answered by adityakothalikar

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).

the ax+by+c=0 from of the line x=-5is ----------​

Answers

the ax+by+c=0 from of the line x=-5is ----------