Find an equation for the line satisfying the given conditions.Through (3, 3) and parallel to 4x - 3y = 6.
y=?
the slope of 4x-3y=6 is 4/3
So, you want a line with slop -3/4
(y-3)/(x-3) = -3/4
rearrange that as you will
4/3x -1
Since the new line is parallel to 4x-3y = 6, it will differ only in the constant
let new line be 4x-3y = k
but (3,3) lies on it, so
12 - 9 = k - 3
new equation: 4x - 3y = 3
or
3y = 4x - 3
y = (4/3)x - 1
To find the equation of a line parallel to a given line, we need the slope of the given line. The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
First, let's rearrange the given equation 4x - 3y = 6 into the form y = mx + b:
4x - 3y = 6
-3y = -4x + 6
y = (4/3)x - 2
From the rearranged equation, we can see that the slope of the given line is 4/3.
Since we want to find a line parallel to this one, the slope will also be 4/3.
Now that we have the slope, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line.
We are given the point (3, 3), so we can substitute these values into the point-slope form:
y - 3 = (4/3)(x - 3)
Now, let's simplify the equation:
y - 3 = (4/3)x - 4
y = (4/3)x - 4 + 3
y = (4/3)x - 1
Therefore, the equation of the line parallel to 4x - 3y = 6 and passing through the point (3, 3) is y = (4/3)x - 1.