Please help me.
Find the equation of the line satisfying the indicated properties. Express your answer in
slope-intercept form.
Passing through point (-2, 4) and perpendicular to the line containing points (3, -1) and (5, -1).
slope of line through (3,-1) and (5,-1) = 0
which is a horizontal line
so our new line is a vertical line, thus the slope is undefined
it must pass through (-2,4) and its equation would simply be
x = -2
(A vertical line cannot be expressed in the y = mx + b form, and you should not have been instructed to do so)
Thank you so much.
To find the equation of a line passing through a given point and perpendicular to another line, we need to apply a few steps:
Step 1: Find the slope of the given line.
Step 2: Determine the slope of the line perpendicular to the given line.
Step 3: Use the point-slope form of the equation of a line to find the equation of the line.
Step 1: Find the slope of the given line.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Using the points (3, -1) and (5, -1), we can calculate the slope of the given line:
slope = (-1 - (-1)) / (5 - 3)
= 0 / 2
= 0
Step 2: Determine the slope of the line perpendicular to the given line.
The slope of a line perpendicular to another line is the negative reciprocal of its slope. So, the slope of the line perpendicular to the given line is -1/0.
Step 3: Use the point-slope form of the equation of a line to find the equation of the line.
The equation of a line in point-slope form is given by:
y - y1 = m(x - x1)
where (x1, y1) is the given point, and m is the slope.
Using the point (-2, 4) and the slope -1/0, we can substitute these values into the point-slope form to find the equation of the line:
y - 4 = (-1/0)(x - (-2))
y - 4 = (-1/0)(x + 2)
Since the slope is undefined (division by zero is undefined), we have a vertical line. To represent a vertical line passing through the point (-2, 4), the equation can be written as:
x = -2
Therefore, the equation of the line passing through the point (-2, 4) and perpendicular to the given line is x = -2.