write an equation of the line containing the given point and parrallel to the given line (6,-4)8x-3y=2
-8x-3y=2
-3y=2-8x
y=(8/3)x+2
so the slope of the given line is 8/3 and since the line is parallel, it will have the same slope. now we can use the given point to solve for b
y=mx+b
y=(8/3)x+b
-4=(8/3)(6)+b
12=b
To find the equation of a line parallel to the given line (8x - 3y = 2) and passing through the point (6, -4), we need to follow these steps:
Step 1: Determine the slope of the given line.
The given line is in standard form (Ax + By = C), so we need to rearrange it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
8x - 3y = 2
-3y = -8x + 2
Divide both sides by -3:
y = (8/3)x - 2/3
The slope of the given line is 8/3.
Step 2: Determine the slope of the line parallel to the given line.
Since the line we want is parallel to the given line, it will have the same slope. Therefore, the slope of the parallel line is also 8/3.
Step 3: Write the equation of the line using the point-slope form.
The equation of a line in point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line.
Using the point (6, -4) and the slope 8/3, we have:
y - (-4) = (8/3)(x - 6)
y + 4 = (8/3)(x - 6)
This is the equation of the line parallel to the given line (8x - 3y = 2) and passing through the point (6, -4).
To find the equation of a line that is parallel to a given line, we need to know that parallel lines have the same slope.
The given line has the equation 8x - 3y = 2. To find the slope of this line, we can rearrange the equation into the slope-intercept form, which is y = mx + b (where m is the slope and b is the y-intercept).
Starting with 8x - 3y = 2, we can isolate y by subtracting 8x from both sides:
-3y = -8x + 2
Now, divide the entire equation by -3 to solve for y:
y = (8/3)x - 2/3
The slope of the given line is 8/3.
Since we want to find a line parallel to this one, we can use the slope-intercept form and the given point (6, -4) to calculate the new equation.
Using the point-slope form of a line, which is y - y1 = m(x - x1), we substitute the values of the given point (x1, y1) = (6, -4) and the slope (m = 8/3) into the equation:
y - (-4) = (8/3)(x - 6)
Simplifying further, we get:
y + 4 = (8/3)(x - 6)
To get the equation in standard form, we can distribute (8/3) to the terms inside the parentheses:
y + 4 = (8/3)x - 16/3
Rearranging the equation, we can subtract y and add 16/3 to both sides:
(8/3)x - y = 16/3 - 4
Multiplying both sides by 3 to clear the fraction, we have:
8x - 3y = 32 - 12
Simplifying further, we get:
8x - 3y = 20
Therefore, the equation of the line containing the point (6, -4) and parallel to the given line 8x - 3y = 2 is 8x - 3y = 20.