Write the equation of the line that passes through the given point and is perpendicular to the given line. Your answer should be written in slope-intercept form.
P(3, −4), x = − 7/8y + 3
your given line has slope -7/8
So a perpendicular line has slope 8/7
Now you have a point and a slope, so the equation is
y+4 = 8/7 (x-3)
now rearrange to y=mx+b form
how do i do that im lost on this stuff
really?
y+4 = 8/7 (x-3)
y+4 = 8/7 x - 24/7
y = 8/7 x - 24/7 - 4
y = 8/7 x - 52/7
You have only learned a few rules for this stuff, so you know that whatever they ask you to do will look a lot like examples they have already given you. Like anything else you are good at, it just takes practice.
Thank you im online so i have to learn reading and practice and go to tutor but they take forever to get back to students
To find the equation of a line perpendicular to a given line, you need to determine the slope of the given line and then find the negative reciprocal of that slope.
First, let's determine the slope of the given line, which is in the form of "x = mx + b". In this case, the slope (m) is equal to -7/8.
To find the negative reciprocal of -7/8, we flip the fraction and change its sign. Thus, the negative reciprocal is 8/7.
Now, we have the slope (m) for the line perpendicular to the given line. We also have a point on this line, which is P(3, -4).
Using the slope-intercept form of a line, which is y = mx + b, we can substitute the values we have into the equation.
The slope (m) of the new line is 8/7 and the point (x, y) is (3, -4). Let's substitute these values into the equation:
y = (8/7)x + b
Now, we need to find the y-intercept (b) of the line. To do that, we can substitute the coordinates of the point (3, -4) into the equation:
-4 = (8/7)(3) + b
Simplifying the equation:
-4 = 24/7 + b
To isolate b, subtract 24/7 from both sides:
-4 - 24/7 = 24/7 - 24/7 + b
Multiplying -4 by 7/7 and simplifying:
-28/7 - 24/7 = b
Combining like terms:
-52/7 = b
Now, we have the value of b. Substitute this value back into the equation:
y = (8/7)x - 52/7
Therefore, the equation of the line that passes through the point P(3, -4) and is perpendicular to the line x = -7/8y + 3 is y = (8/7)x - 52/7.