What is the equation of the line parallel to 4x - 3y = 8 and passing through the point (5, - 1) ?
A. y - 5 = 4/3 (x + 1)
B. y + 1 = 4/3 (x - 5)
C. y + 1 = -3/4 (x - 5)
D. y - 5 = -3/4 (x + 1)
3 y = 4 x - 8
y = (4/3) x - 8/3
slope = 4/3
same slope for our line
(y+1) / (x-5) = 4/3
Well, let me have a clown's guess at this one! To find a line parallel to the given line, we need to keep the same slope. The given equation can be rewritten as 4x - 8 = 3y, then y = (4/3)x - (8/3). So the slope of the given line is 4/3.
Now, let's look at the answer choices. Option A has the right slope, but do the numbers work? Substituting the point (5, -1) into the equation, we get -6 = 6, which is not true. So we can clown around and eliminate that one.
What about option B? It has the right slope and substituting (5, -1) gives us -2 = -2. That's clown-tastic! So option B seems like the winner!
To put it in math terms, the equation of the line parallel to 4x - 3y = 8 and passing through the point (5, -1) is y + 1 = 4/3 (x - 5). So the answer is option B. Keep clowning around!
To find the equation of a line parallel to 4x - 3y = 8, we need to find the slope of the given line. The equation is in the form of Ax + By = C, where A, B, and C are constants. So, we need to rearrange the equation in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Given equation: 4x - 3y = 8
Rearranging the equation, we get: 3y = 4x - 8
Dividing both sides by 3, we get: y = (4/3)x - (8/3)
From this equation, we can see that the slope of the line is 4/3.
Since the line we want is parallel to this line, it will have the same slope of 4/3.
Next, we need to use the point-slope form of a line to find the equation of the line passing through the point (5, -1) with the slope of 4/3.
The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values, we get: y - (-1) = (4/3)(x - 5)
Simplifying, we get: y + 1 = (4/3)(x - 5)
Therefore, the equation of the line parallel to 4x - 3y = 8 and passing through the point (5, -1) is option B: y + 1 = (4/3)(x - 5).
To find the equation of a line parallel to another line, we need to use the fact that parallel lines have the same slope.
First, let's rearrange the given equation of the line, 4x - 3y = 8, into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Start by isolating y:
4x - 3y = 8
-3y = -4x + 8
Divide through by -3 to solve for y:
y = (4/3)x - 8/3
Now we know the slope of the given line is 4/3. Since the line we are looking for is parallel to this line, it will also have a slope of 4/3.
Using the point-slope form of a line (y - y₁ = m(x - x₁)), where (x₁, y₁) is any point on the line, we can substitute the given point (5, -1) and the slope of 4/3 into the equation:
y - (-1) = (4/3)(x - 5)
y + 1 = (4/3)(x - 5)
Now we can simplify the equation:
y + 1 = (4/3)x - 20/3
To put the equation in the standard form, let's get rid of the fractions by multiplying through by 3:
3(y + 1) = 4x - 20
3y + 3 = 4x - 20
Rearrange the equation to get it in the form Ax + By = C:
4x - 3y - 23 = 0
Therefore, the equation of the line parallel to the original line and passing through the point (5, -1) is given by option D:
D. y - 5 = -3/4 (x + 1)