Write an equation of the line containing the given point and parallel to the given line.
(6,−3); 8x−9y=4
parallel lines have the same slope
8x−9y=4 has slope m = 8/9
so, using the point-slope form, the line with that slope through (6,-3) is
y+3 = 8/9 (x-6)
or ...
Since parallel, the 2 line equations differ only in the constant, so ...
8x - 9y = c , ..... just plug in the point (6,-3)
48 + 27 = c = 75
8x - 9y = 75
To find the equation of a line parallel to the given line, we need to determine the slope of the given line. The equation of a line can be written in slope-intercept form (y = mx + b), where 'm' represents the slope of the line.
Given line: 8x - 9y = 4
To determine the slope, we need to rearrange the given equation in slope-intercept form:
-9y = -8x + 4
Dividing by -9:
y = (8/9)x - 4/9
The slope of the given line is (8/9).
Since a line parallel to the given line will have the same slope, the equation of the parallel line can be written as:
y = (8/9)x + b
To determine the value of 'b', we can substitute the coordinates of the given point (6, -3) into the equation.
-3 = (8/9)(6) + b
-3 = 16/3 + b
To isolate 'b', we can subtract 16/3 from both sides:
-3 - 16/3 = b
(-9-16)/3 = b
-25/3 = b
Therefore, the equation of the line parallel to the given line, containing the point (6, -3) is:
y = (8/9)x - 25/3
To find the equation of a line parallel to a given line, we need to determine the slope of the given line.
The given line has the equation 8x - 9y = 4. To start, we rearrange the equation to be in the slope-intercept form (y = mx + b), where m represents the slope of the line:
8x - 4 = 9y
(8/9)x - 4/9 = y
From the rearranged equation, we observe that the slope of the given line is 8/9.
Since a line parallel to the given line will have the same slope, we can use this slope along with the given point (6, -3) to write the equation of the parallel line.
Using the point-slope form (y - y1 = m(x - x1)), where (x1, y1) is the given point and m is the slope, we have:
y - (-3) = (8/9)(x - 6)
y + 3 = (8/9)(x - 6)
Finally, we can rearrange the equation to the slope-intercept form:
y + 3 = (8/9)x - 16/3
y = (8/9)x - 16/3 - 9/3
y = (8/9)x - 25/3
Therefore, the equation of the line containing the given point (6, -3) and parallel to the line 8x - 9y = 4 is y = (8/9)x - 25/3.