Answer:
y=2/5x + 33/5
Explanation:
To find the equation of the line that passes through the point (-9,3) and is perpendicular to y = 1/2x + 6, we can first find the slope of the given line y = 1/2x + 6. The slope of a line is equal to the rise (the change in the y-coordinate) divided by the run (the change in the x-coordinate), so we can find the slope of the line y = 1/2x + 6 as follows:
Slope = (change in y) / (change in x)
= (1/2 - 6) / (1 - 0)
= -5/2
Since the line we are looking for is perpendicular to the line y = 1/2x + 6, its slope must be the negative reciprocal of the slope of y = 1/2x + 6. The negative reciprocal of a number is equal to the negative of the reciprocal of the number, so the slope of the line we are looking for is equal to -1 / (-5/2) = 2/5.
Next, we can use the point-slope form of a line to find the equation of the line that passes through the point (-9,3) and has a slope of 2/5. The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Substituting the values for the given point and the slope into this equation, we get:
y - 3 = 2/5(x - (-9))
y - 3 = 2/5(x + 9)
Next, we can distribute the 2/5 on the right-hand side of the equation to get:
y - 3 = 2/5x + 18/5
Finally, we can combine like terms on both sides of the equation to get the final equation of the line:
y=2/5x + 18/5 + 3
y=2/5x + 33/5