What is the equation of the line perpendicular to the line y = four-ninthsx – 2 that passes through the point (4,3)?
(1 point)
Responses
y = –four-ninthsx – 2
y = – Image with alt text: four-ninths x – 2
y = nine-fourthsx + 6
y = Image with alt text: nine-fourths x + 6
y = –nine-fourthsx + 12
y = – Image with alt text: nine-fourths x + 12
y = –nine-fourthsx – 12
The correct answer is y = –nine-fourthsx + 12
To find the equation of the line perpendicular to the given line, we need to determine the slope of the given line first. The slope of a line in the form y = mx + c represents the coefficient of x, which is four-ninths in this case.
For lines to be perpendicular, the product of their slopes should be -1. Therefore, the slope of the line perpendicular to the given line would be the negative reciprocal of four-ninths.
The negative reciprocal of four-ninths is -9/4.
Now that we have the slope (-9/4) and the point (4,3) that the line passes through, we can use the point-slope form of a line to find the equation.
y - y1 = m(x - x1)
Where (x1, y1) is the point (4,3) and m is the slope (-9/4).
Plugging in the values, the equation becomes:
y - 3 = -9/4(x - 4)
Simplifying,
y - 3 = -9/4x + 9
y = -9/4x + 12
Therefore, the equation of the line perpendicular to the given line and passing through the point (4,3) is:
y = -9/4x + 12