** Parallel and Perpendicular Lines Equations
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4x Find the equation of the line parallel to the line shown in the graph passing through the point (-2,
3).
4x
4x B
4x C
4x
x
Ay-x
4x
*
ys
ys
B
2 13
MIN
4x Find the equation of the line perpendicular to the line shown in the graph passing through the point
(-2,3).
y=
2
123
A yox
13
13
3 13
Cy=²x-3
Dy=-x+3
To find the equation of a line parallel to the given line, we first need to determine the slope of the given line. Let's call the given line "Line A." Since the graph is not provided, I'll assume Line A has an equation of the form y = mx + b, where m is the slope and b is the y-intercept.
1. Find the slope (m) of Line A:
Since the equation is not provided, we cannot find the exact value of m. However, we know that parallel lines have the same slope. So the slope of the line we need to find will be the same as Line A's slope.
2. Use the point (-2, 3) and the same slope (m) to find the equation of the parallel line:
The equation for a line in slope-intercept form is y = mx + b. We know the slope (m) and a point on the line (x = -2 and y = 3). Plug in these values:
3 = m(-2) + b
Solve for b:
b = 3 + 2m
So the equation of the parallel line is:
y = mx + (3 + 2m)
3. Find the equation of the line perpendicular to Line A:
Perpendicular lines have slopes that are negative reciprocals of each other. So, if Line A has a slope of m, the perpendicular line's slope will be -1/m.
4. Use the point (-2, 3) and the slope -1/m to find the equation of the perpendicular line:
3 = (-1/m)(-2) + b
Solve for b:
b = 3 + (2/m)
So the equation of the perpendicular line is:
y = (-1/m)x + (3 + 2/m)
Since we do not have the specific equation for the given line (Line A), we cannot find exact equations for the parallel and perpendicular lines. However, the general equations are:
Parallel line: y = mx + (3 + 2m)
Perpendicular line: y = (-1/m)x + (3 + 2/m)