What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, −3)?
Point-slope form : y-y₁=m(x-x₁)
Perpendicular to the given line, and passes through (-4, -3)
Given line slope : -4
How we found slope : I found 2 exact points, and found the slope by doing the slope formula (y₂-y₁/x₂-x₁)
m = slope
However, when a line is perpendicular, we must find the negative reciprocal of our slope.
Slope₁ = -4
Slope ₂ = 1/4
Simply plug everything in.
y - y₁ = m(x - x₁)
y + 3 = 1/4(x +4)
The slope was not given, (there was no "given line").
Veronica's answer is partially correct, except there was no way of finding the slope.
I suspect the student tried to copy and paste the original equation.
To find the equation of a line that is perpendicular to a given line and passes through a given point, you need to follow these steps:
Step 1: Determine the slope of the given line.
The equation of the given line is usually in the form y = mx + b, where 'm' represents the slope. If the given line equation is not in this form, rearrange it to this form and identify the slope.
Step 2: Find the negative reciprocal of the slope.
To get the slope of a line perpendicular to another line, take the negative reciprocal of the slope of the given line. The negative reciprocal is obtained by flipping the fraction and changing the sign. For example, if the slope of the given line is m, then the perpendicular line's slope would be -1/m.
Step 3: Plug the values into the point-slope form equation.
Once you have the slope of the perpendicular line and a point it passes through, you can use the point-slope form equation y - y1 = m(x - x1). Here, (x1, y1) represents the coordinates of the given point, and 'm' represents the slope found in step 2.
Now, let's apply these steps to your problem:
Step 1: Determine the slope of the given line.
Since the equation of the given line is not provided in your question, you'll need to find it or assume its value.
Step 2: Find the negative reciprocal.
Once you have the slope of the given line, invert it and change its sign to obtain the negative reciprocal slope.
Step 3: Plug the values into the point-slope form equation.
Using the negative reciprocal slope and the coordinates (-4, -3) of the given point, substitute them into the point-slope form equation y - y1 = m(x - x1).
This will give you the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4, -3).