Give the equation of a line perpendicular to the line y = 4x having the same y-intercept.
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I don't even know where or how to start.Im lost on these.
This is a test your teacher gave you. If you don't know where to start, you need to fail it. Getting answers from others will just put you in a deeper hole. Discuss this situation with your teacher.
The series of questions you asked are routine questions.
If you are finishing a semester and are reviewing for exams, you should know how to do these.
For the above question,
- how are slopes of perpendicular lines related ?
- what point is associated with the y-intercept of an equation of the form
y = mx + b ?
The y intercept of your y = 4x line is zero, and since the second line also has that y intercept, both lines must go through the origin (0,0).
The product of the slopes (m) for the two lines must be -1, if they are perpendicular. The first line has a slope of 4. You should be able to figure out the rest of it.
To find the equation of a line perpendicular to y = 4x with the same y-intercept, we need to determine the slope of the perpendicular line first.
The given line has a slope of 4. To find the slope of a line perpendicular to y = 4x, we take the negative reciprocal of the slope. So, the perpendicular line will have a slope of -1/4.
Let's assume the y-intercept of the perpendicular line is b.
The equation of a line can be represented in the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Now, we have the slope (m = -1/4) and the y-intercept (b = given y-intercept).
Therefore, the equation of the line perpendicular to y = 4x with the same y-intercept is:
y = (-1/4)x + b, where b is the y-intercept of the original line y = 4x.