Write an equation of the line containing the given point and parellel to the given line.
(2,-6); 9x-5y=4
rearranging the given line,
y = (9/5)x - 4/5 (1)
which has the form
y = mx + b (2)
where m is the slope and b is the y intercept.
The new line would have the same slope to be parallel, so it would have the form:
y = (9/5)x + b (3)
to solve for b, input the given coordinates, obtaining:
(-6) = (9/5)(2) + b
rearrange and solve for b, then substitute back into equation (3)
It looks like b = -30/5 -18/5 = -48/5
So
y = (9/5)x - 48/5
(or 9x-5y=48)
Check: when x = 2,
y = 18/5 - 48/5 = -30/5 = -6
Looks OK
The new equation must be something like
9x - 5y = c
plug in the given point(2,-6)
18 + 30 = c = 48
all done : 9x - 5y = 48
To find the equation of a line parallel to the given line, we need to know that parallel lines have the same slope. The given line is in the form of "Ax + By = C", where A, B, and C are constants.
Step 1: Determine the slope of the given line
For a line in the form of "Ax + By = C", we can rearrange it to the slope-intercept form "y = mx + b" by solving for y:
9x - 5y = 4
-5y = -9x + 4
y = (9/5)x - 4/5
From this equation, we can see that the slope of the given line is 9/5.
Step 2: Write the equation of the line parallel to the given line
Since the parallel line has the same slope, we know the slope is also 9/5.
Now, we can use the point-slope form of a linear equation to write the equation of the line parallel to the given line. The point-slope form is given by:
y - y1 = m(x - x1)
Substituting the given point (2,-6) and the slope (9/5) into the point-slope form, we get:
y - (-6) = (9/5)(x - 2)
y + 6 = (9/5)x - (18/5)
To simplify the equation, we can multiply through by 5 to get rid of the fractions:
5(y + 6) = 9x - 18
5y + 30 = 9x - 18
Finally, we can rearrange this equation into the standard form "Ax + By = C":
9x - 5y = 48
Therefore, the equation of the line containing the given point (2,-6) and parallel to the given line 9x-5y=4 is 9x - 5y = 48.