consider the line 8x-5y=-4
find the equation of the line that is perpendicular to this line and passes through the point (-4,-4)
find the equation of the line that is parallel to this line and passes through the point (-4, -4)
i keep getting different answers on the perpendicular and parallel equations can anybody help?
5 y = 8 x + 4
y = (8/5) x + 4/5
so slope is 8/5
so slope of perpendicular is -5/8
form is
y = - 5x/8 + b
goes through (-4,-4)
-4 = -5 (-4)/8 + b
b = -4 - 20/8
b = -4 - 5/2
b = -8/2-5/2 = -13/2
so
y = - 5 x/8 -13/2
or
8y = -5 x - 52
Now parallel line
slope = 8/5
y = 8 x/5 + b
-4 = -32 /5 + b
-20/5 = -32 /5 + b
b = 12 /5
so
y = 8 x/5 + 12/5
or
5 y = 8 x + 12
Why, of course I can help! But just remember, my answers might be a little clownish.
Let's start with the line perpendicular to the given line. To find this, we need to determine the slope of the original line and then find the negative reciprocal of that slope. So, let's rearrange the given equation into slope-intercept form (y = mx + b), where m represents the slope:
8x - 5y = -4
-5y = -8x - 4
y = (8/5)x + (4/5)
Now, we can see that the slope of the original line is 8/5. To find the slope of the line perpendicular to this, we can take the negative reciprocal of 8/5. So, the slope of the perpendicular line is -5/8.
Using the point-slope form of a linear equation (y - y1 = m(x - x1)) and plugging in the given point (-4, -4), we can write the equation for the line perpendicular to the given line:
y - (-4) = (-5/8)(x - (-4))
y + 4 = (-5/8)(x + 4)
Now let's move on to the line parallel to the given line. Parallel lines have the same slope. So, if we rearrange the given equation into slope-intercept form again:
8x - 5y = -4
-5y = -8x - 4
y = (8/5)x + (4/5)
We can see that the slope of the original line is 8/5. So, the line parallel to this will have the same slope, which is 8/5.
Using the point-slope form and the point (-4, -4), the equation for the line parallel to the given line is:
y - (-4) = (8/5)(x - (-4))
y + 4 = (8/5)(x + 4)
I hope that clarifies things a little, but remember, with clown math, anything can happen!
To find the equation of the line that is perpendicular to the given line, we need to determine the slope of the given line and then find the negative reciprocal of this slope. Let's solve the equation 8x - 5y = -4 for y to determine the slope:
8x - 5y = -4
-5y = -8x - 4
y = (8/5)x + 4/5
From this equation, we can see that the slope of the given line is 8/5. To find the slope of the perpendicular line, we take the negative reciprocal of 8/5, which is -5/8.
Now, we will use the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is a given point and m is the slope. Plugging in the point (-4, -4) and the slope -5/8, we have:
y - (-4) = -5/8(x - (-4))
y + 4 = -5/8(x + 4)
y + 4 = -5/8x - 5/2
y = -5/8x - 5/2 - 4
y = -5/8x - 13/2
Therefore, the equation of the line that is perpendicular to the given line and passes through the point (-4, -4) is y = -5/8x - 13/2.
To find the equation of the line that is parallel to the given line, we can use the same point-slope form of the equation of a line. With the same point (-4, -4) and the slope of the given line (8/5) as the slope, the equation becomes:
y - (-4) = 8/5(x - (-4))
y + 4 = 8/5(x + 4)
y + 4 = 8/5x + 32/5
y = 8/5x + 32/5 - 4
y = 8/5x + 32/5 - 20/5
y = 8/5x + 12/5
Therefore, the equation of the line that is parallel to the given line and passes through the point (-4, -4) is y = 8/5x + 12/5.
To find the equation of the line that is perpendicular to the given line and passes through the point (-4, -4), we need to follow these steps:
Step 1: Find the slope of the given line.
In order to find the slope of the given line, we need to rewrite the equation in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Let's rearrange the given equation:
8x - 5y = -4
-5y = -8x - 4
y = (8/5)x + 4/5
From this form, we can see that the slope of the given line is 8/5.
Step 2: Find the negative reciprocal of the slope.
To find the slope of the line perpendicular to the given line, we need to take the negative reciprocal of the slope of the given line.
The negative reciprocal is obtained by flipping the fraction and changing the sign.
The negative reciprocal of 8/5 is -5/8.
Step 3: Use the point-slope form to write the equation.
Now that we have the slope (-5/8) and the given point (-4, -4), we can use the point-slope form to write the equation:
y - y1 = m(x - x1), where (x1, y1) represents the given point and m represents the slope.
Substituting the values, we get:
y - (-4) = (-5/8)(x - (-4))
y + 4 = (-5/8)(x + 4)
Expanding and rearranging, we find:
y + 4 = (-5/8)x - 5/2
y = (-5/8)x - 5/2 - 4
y = (-5/8)x - 13/2
So, the equation of the line that is perpendicular to the given line and passes through the point (-4, -4) is y = (-5/8)x - 13/2.
Now, to find the equation of the line that is parallel to the given line and passes through the point (-4, -4), we can follow these steps:
Step 1: Use the given point to find the y-intercept.
Substitute the given point (-4, -4) into the equation of the given line:
8x - 5y = -4
8(-4) - 5(-4) = -4
-32 + 20 = -4
-12 = -4
So, the y-intercept is -4.
Step 2: Write the equation in slope-intercept form.
Since we know the slope of the given line is 8/5, and we have the y-intercept (-4), we can write the equation of the line in slope-intercept form:
y = (8/5)x - 4
Therefore, the equation of the line that is parallel to the given line and passes through the point (-4, -4) is y = (8/5)x - 4.