Question
Write the equation in standard form line through (0,2) perpendicular to y=5/2x+2
Answers
GPT 3.5
To find the equation of a line perpendicular to y = (5/2)x + 2 and passing through the point (0, 2), we need to find the slope of the perpendicular line.
The slope of the original line is (5/2). The slope of a line perpendicular to this line can be found by taking the negative reciprocal of (5/2).
The negative reciprocal of (5/2) is -(2/5).
Now we have the slope of the perpendicular line, which is -(2/5), and the point it passes through, (0, 2).
Using the point-slope form of a line, which is y - y1 = m(x - x1), we can plug in the values to find the equation of the line.
y - 2 = -(2/5)(x - 0)
Simplifying, we have:
y - 2 = -(2/5)x
To express the equation in standard form, we multiply through by 5 to eliminate the fraction:
5y - 10 = -2x
Rearranging the terms, we get:
2x + 5y = 10
Therefore, the equation of the line in standard form that passes through (0, 2) and is perpendicular to y = (5/2)x + 2 is 2x + 5y = 10.
The slope of the original line is (5/2). The slope of a line perpendicular to this line can be found by taking the negative reciprocal of (5/2).
The negative reciprocal of (5/2) is -(2/5).
Now we have the slope of the perpendicular line, which is -(2/5), and the point it passes through, (0, 2).
Using the point-slope form of a line, which is y - y1 = m(x - x1), we can plug in the values to find the equation of the line.
y - 2 = -(2/5)(x - 0)
Simplifying, we have:
y - 2 = -(2/5)x
To express the equation in standard form, we multiply through by 5 to eliminate the fraction:
5y - 10 = -2x
Rearranging the terms, we get:
2x + 5y = 10
Therefore, the equation of the line in standard form that passes through (0, 2) and is perpendicular to y = (5/2)x + 2 is 2x + 5y = 10.