Post a New QuestionCurrent Questions
Homework Help: Math
Posted by Mikil on Wednesday, September 23, 2015 at 6:50pm.
Write a linear equation in slope intercept form for each of the following:
A line perpendicular to y=x+2 that passes through the origin.
A line perpendicular to y = -1/2x + 5 that passes through the points (4,1) and (1,-5).
A line that is the perpendicular bisector of a segment whose endpoints are (3,5) and (7,1).
Answer this Question
see previous post for method and example
Hint:
What have you learned about the slopes of perpendicular lines ?
in the form y = mx + b, what does the m stand for ?
To write a linear equation in slope-intercept form, you need to find the slope and the y-intercept of the line.
For the first question, you have a line perpendicular to y = x + 2 that passes through the origin.
To find the slope of the given line, you can rewrite it in slope-intercept form (y = mx + b), where the coefficient of x is the slope. In this case, the slope is 1.
Since the line is perpendicular, the slope of the new line will be the negative reciprocal of the given slope. Therefore, the slope of the new line will be -1.
Now, we know that the new line passes through the origin, which means the coordinates (0,0) satisfy the equation of the line.
Using the point-slope form (y - y1 = m(x - x1)), we can substitute the values into the equation.
y - 0 = -1(x - 0)
y = -x
The linear equation in slope-intercept form for the line perpendicular to y = x + 2 and passing through the origin is y = -x.
For the second question, you have a line perpendicular to y = -1/2x + 5 that passes through the points (4,1) and (1,-5).
To find the slope of the given line, you can rewrite it in slope-intercept form (y = mx + b), where the coefficient of x is the slope. In this case, the slope is -1/2.
Since the line is perpendicular, the slope of the new line will be the negative reciprocal of the given slope. Therefore, the slope of the new line will be 2.
Now, we can use the point-slope form (y - y1 = m(x - x1)) and substitute the values of one of the given points into the equation. Let's choose the point (4,1).
y - 1 = 2(x - 4)
y - 1 = 2x - 8
y = 2x - 7
The linear equation in slope-intercept form for the line perpendicular to y = -1/2x + 5 and passing through the points (4,1) and (1,-5) is y = 2x - 7.
For the third question, you have a line that is the perpendicular bisector of a segment whose endpoints are (3,5) and (7,1).
To find the midpoint of the segment, you can use the midpoint formula ((x1 + x2)/2, (y1 + y2)/2). Let's calculate the midpoint:
Midpoint = ((3 + 7)/2, (5 + 1)/2)
Midpoint = (5, 3)
Now, to find the slope of the segment, you can use the formula (y2 - y1)/(x2 - x1). Let's calculate the slope:
Slope = (1 - 5)/(7 - 3)
Slope = -4/4
Slope = -1
Since the line is perpendicular, the slope of the new line will be the negative reciprocal of the given slope. Therefore, the slope of the new line will be 1.
Now, using the point-slope form (y - y1 = m(x - x1)) and substituting the values of the midpoint into the equation, we can find the linear equation.
y - 3 = 1(x - 5)
y - 3 = x - 5
y = x - 2
The linear equation in slope-intercept form for the line that is the perpendicular bisector of the segment whose endpoints are (3,5) and (7,1) is y = x - 2.