How do I write one equations in slope-intercept form, and three other lines in slope-intercept form that are perpendicular to the first line ??
Please Help, Thank you =)
one line: y=mx+b
second line perpendicular
y= -x/m + c
of course, you have to know m, b, c.
for the second line perpendicular, example if it
-2/3 slope. it will be use for the 3rd and 4th line perpendicular right ? and pick any value of for y-intercept for the 3rd and 4th ?
To write an equation in slope-intercept form, you need to use the formula:
y = mx + b
where:
- y represents the y-coordinate
- m represents the slope
- x represents the x-coordinate
- b represents the y-intercept (the point where the line crosses the y-axis)
To write one equation in slope-intercept form, you need to know the slope (m) and the y-intercept (b). If these values are not given, you will need additional information or given points to find them.
Once you have the equation in slope-intercept form, you can find three other lines that are perpendicular. For two lines to be perpendicular, their slopes must be negative reciprocals of each other. This means you flip the sign of the slope and find the reciprocal of it.
Here's a step-by-step guide:
1. Determine the slope (m) and the y-intercept (b) of the original line. If this information is not provided, you need to use other given points or additional information to find them.
2. Write the equation of the original line in slope-intercept form, using the determined values of m and b.
3. Find the negative reciprocal of the slope of the original line. This will be the slope of the perpendicular lines.
4. Use the slope-intercept form to write the equations of the three perpendicular lines, using the negative reciprocal slope and different y-intercepts.
For example, let's say the equation of the original line is y = 2x + 3.
1. The slope is 2, and the y-intercept is 3.
2. The equation of the original line in slope-intercept form is y = 2x + 3.
3. The negative reciprocal of 2 is -1/2, so the slope of the perpendicular lines is -1/2.
4. You can write three different equations of perpendicular lines using the slope-intercept form, y = (-1/2)x + b, where b is a different y-intercept for each line.
So, for example, the equations of three perpendicular lines could be:
- y = (-1/2)x + 1
- y = (-1/2)x - 2
- y = (-1/2)x + 5
Remember that the key is to find the negative reciprocal of the slope and then use different y-intercepts to write the equations of the perpendicular lines.