write an equation for each line described. Express answers in point slope or slope intercept form.
A) The line perpendicular to the line x=2 passing through the point (-4, 3.3)
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To find the equation of a line that is perpendicular to the line x = 2 and passes through the point (-4, 3.3), we first need to determine the slope of the given line.
The line x = 2 is a vertical line that passes through the point (2, y) for all values of y. Since it is a vertical line, its slope is undefined.
To find the slope of a line that is perpendicular to the line x = 2, we can use the fact that the product of the slopes of two perpendicular lines is -1.
Since the slope of the line x = 2 is undefined, the slope of the line perpendicular to it will be 0.
Now, we can use the point-slope form of a linear equation to find the equation of the line: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using the point (-4, 3.3) and the slope m = 0, we can substitute these values into the point-slope form:
y - 3.3 = 0(x - (-4))
Simplifying:
y - 3.3 = 0(x + 4)
y - 3.3 = 0x + 0
y = 0x + 3.3
Hence, the equation of the line perpendicular to x = 2 and passing through the point (-4, 3.3) is y = 3.3.