What is the equation of the line perpendicular to the line y=4/9x-2 that passes through the point (4,3)
To find the equation of the line perpendicular to y = (4/9)x - 2 and passes through the point (4, 3), we need to find the negative reciprocal of the slope of the given line.
The given line has a slope of 4/9, so the negative reciprocal of the slope is -(9/4).
Using the given point (4, 3) and the new slope -(9/4), we can use the point-slope form of a linear equation to find the equation of the perpendicular line.
The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Substituting the values into the equation, we get:
y - 3 = -(9/4)(x - 4)
Expanding the equation:
y - 3 = -(9/4)x + 9
Bringing like terms to one side:
y = -(9/4)x + 12
Therefore, the equation of the line perpendicular to y = (4/9)x - 2 and passes through the point (4, 3) is y = -(9/4)x + 12.
To find the equation of the line perpendicular to the line y = (4/9)x - 2 that passes through the point (4,3), we need to determine the slope of the perpendicular line.
The given line has a slope of 4/9. The slope of a line perpendicular to this line will be the negative reciprocal of the given slope. So, the perpendicular slope will be -9/4.
Now that we have the slope (-9/4) and a point (4,3), we can use the point-slope form of a linear equation to find the equation of the line.
The point-slope form of a linear equation is given by: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.
Substituting the slope (-9/4) and the point (4,3) into the point-slope form equation, we get:
y - 3 = (-9/4)(x - 4)
To simplify, we distribute the slope:
y - 3 = (-9/4)x + 9
Rearranging the equation to obtain y on one side, we have:
y = (-9/4)x + 9 + 3
Simplifying further:
y = (-9/4)x + 12
Therefore, the equation of the line perpendicular to y = (4/9)x - 2 that passes through the point (4,3) is y = (-9/4)x + 12.
To find the equation of a line perpendicular to the given line and passing through the point (4, 3), you need to determine the slope of the given line and then find the negative reciprocal of that slope.
Step 1: Given line equation: y = (4/9)x - 2
The slope of the given line can be determined by examining the coefficient of the x term, which is 4/9 in this case. So, the slope is m = 4/9.
Step 2: The slope of the perpendicular line is the negative reciprocal of the given line's slope. To find it, invert the fraction and change its sign. Therefore, the perpendicular slope is -9/4.
Step 3: Now, you have the slope (-9/4) and the point (4, 3). To find the equation of the perpendicular line, you can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values, we get:
y - 3 = (-9/4)(x - 4)
Step 4: Simplify the equation:
y - 3 = (-9/4)x + (9/4)(4)
y - 3 = (-9/4)x + 9
y = (-9/4)x + 12
Therefore, the equation of the line perpendicular to y = (4/9)x - 2 and passing through the point (4, 3) is y = (-9/4)x + 12.