Choose the equation of a line that is perpendicular to the given line and that passes through the given point.
4x – 12y = 2; (10, –1)
(1 point)
Responses
a. y = 3x + 29
b. y = –one-thirdx + 29
c. y = –3x + 29
d. y = –one-thirdx + 7
To find the equation of a line that is perpendicular to the given line 4x - 12y = 2, we need to first find the slope of the given line.
Rearrange the equation into slope-intercept form (y = mx + b):
-12y = -4x + 2
y = (1/3)x - 1/6
The slope of the given line is 1/3. To find the slope of the perpendicular line, we use the fact that the product of the slopes of two perpendicular lines is -1.
So the slope of the perpendicular line is the negative reciprocal of 1/3, which is -3.
Now we have the point (10, -1) that the line must pass through and the slope of the line. We will use the point-slope form of a linear equation to find the equation of the line.
y - y1 = m(x - x1)
y - (-1) = -3(x - 10)
y + 1 = -3x + 30
y = -3x + 29
Therefore, the equation of a line that is perpendicular to 4x – 12y = 2 and passes through (10, -1) is y = -3x + 29, which is option c.