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Which of the following is an equation of the line in the
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11 Nov 2020, 09:56
11 Nov 2020, 09:56
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Which of the following is an equation of the line in the xy-plane that passes through the point (0, −3) and is perpendicular to the line y = −4x + 7?
A. y = −4x − 6
B. y = −4x − 3
C. y = −4x + 3
D. y = \(\frac{1}{4}\) x − 3
E. y = \(\frac{1}{4}\) x + 6
Source: 320 GRE Math Questions
A. y = −4x − 6
B. y = −4x − 3
C. y = −4x + 3
D. y = \(\frac{1}{4}\) x − 3
E. y = \(\frac{1}{4}\) x + 6
Source: 320 GRE Math Questions
Re: Which of the following is an equation of the line in the
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11 Nov 2020, 20:24
11 Nov 2020, 20:24
1
we know it two straight lines are perpendicular to each-other having slops m1 and m2, then
m1*m2=-1. Here, the equation of one line is given; Y=-4*X+C, thus, its slope, m1= -4
which implies, m2=1/4, let the equation be; Y=1/4*X+C1 that passes through (0,-3) point,
therefore, putting the values of X=0 and Y=-3 in the above equation we get the value of
C1= -3 and ultimately the equation will be, Y=1/4*X-3 (D is the answer)
m1*m2=-1. Here, the equation of one line is given; Y=-4*X+C, thus, its slope, m1= -4
which implies, m2=1/4, let the equation be; Y=1/4*X+C1 that passes through (0,-3) point,
therefore, putting the values of X=0 and Y=-3 in the above equation we get the value of
C1= -3 and ultimately the equation will be, Y=1/4*X-3 (D is the answer)
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Re: Which of the following is an equation of the line in the
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31 May 2023, 23:53
31 May 2023, 23:53
↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧
We need to find equation of the line in the xy-plane that passes through the point (0, −3) and is perpendicular to the line y = −4x + 7
Let's find the slope of line y = −4x + 7
We know that generic equation of a line is y = mx + b (Where m is the slope of the line)
=> Slope of line y = −4x + 7 = -4
Now, the line whose equation we have to find is perpendicular to y = −4x + 7
=> Slope,m of this line can be found by m * -4 = -1
=> m = \(\frac{1}{4}\)
Equation of a line passing through the point (0, -3) and having a slope of \(\frac{1}{4}\) is given by
y - \(y_1\) = m * (x - \(x_1\))
=> y - (-3) = \(\frac{1}{4}\) * (x - 0)
=> y + 3 = \(\frac{1}{4}\) x
=> \(y =\frac{ 1}{4} x − 3\)
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Slope of a Line
We need to find equation of the line in the xy-plane that passes through the point (0, −3) and is perpendicular to the line y = −4x + 7
Let's find the slope of line y = −4x + 7
We know that generic equation of a line is y = mx + b (Where m is the slope of the line)
=> Slope of line y = −4x + 7 = -4
Now, the line whose equation we have to find is perpendicular to y = −4x + 7
=> Slope,m of this line can be found by m * -4 = -1
=> m = \(\frac{1}{4}\)
Equation of a line passing through the point (0, -3) and having a slope of \(\frac{1}{4}\) is given by
y - \(y_1\) = m * (x - \(x_1\))
=> y - (-3) = \(\frac{1}{4}\) * (x - 0)
=> y + 3 = \(\frac{1}{4}\) x
=> \(y =\frac{ 1}{4} x − 3\)
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Slope of a Line
