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 ??
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one line: y=mx+b
second line perpendicular
y= -x/m + c
of course, you have to know m, b, c.
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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, follow these steps:
Step 1: Identify the slope (m) and the y-intercept (b) of the given line.
Step 2: Write the equation as y = mx + b, replacing m with the slope and b with the y-intercept.
Now, to find three other lines that are perpendicular to the first line:
Step 3: Determine the negative reciprocal of the slope of the given line, which will be the slope of the perpendicular lines. This can be done by taking the negative value of the reciprocal of the original slope.
Step 4: Use the new slope value to write the equations of the three perpendicular lines in slope-intercept form, keeping in mind that the y-intercept can be any value (represented by c in the equation).
For example, let's say the equation of the first line is y = 2x + 3.
Step 1: The slope (m) is 2, and the y-intercept (b) is 3.
Step 2: Writing the equation in slope-intercept form, we have y = 2x + 3.
Step 3: The negative reciprocal of the slope (2) is -1/2. So the slope of the perpendicular lines will be -1/2.
Step 4: We can choose any value for the y-intercept (c) for the perpendicular lines. Let's say we choose c = 5.
Therefore, the equations of the three other lines that are perpendicular to the first line are:
y = -1/2x + 5
y = -1/2x + 5
y = -1/2x + 5
Note that all three lines have the same slope (-1/2) and different y-intercepts (c = 5), as per the example given.