Could someone please help me write an equation of the line containing the given point and parallel to the given line.
(6,-9)4x-5y=8
Y=?
Note that when two lines are parallel, their slopes are equal. The given equation is 4x - 5y = 8. To get its slope, we change it to the form
y = mx + b
where m is the slope and b is the y-intercept. Therefore,
4x - 5y = 8
-5y = -4x + 8
y = (4/5)x - 8/5
The slope is equal to 4/5. Thus the slope of the line passing through the point (6, -9) is also 4/5.
Now to get the equation of line, recall that given a slope and a point on the line, we the point-slope form:
y - y1 = m(x - x1)
where (x1, y1) is the point. Substituting,
y - (-9) = (4/5)(x - 6)
y + 9 = (4/5)x - 24/5
y = (4/5)x - 24/5 - 9 ; note that 9 is also 45/5
y = (4/5)x - 69/5
Hope this helps~ :3
easiest way:
As Jai pointed out , the two lines are parallel so their equations must differ only in the constant
let the new equation be 4x - 5y = c
but (6,-9) lies on it, so
24 + 45 = c = 69
new equation: 4x - 5y = 69
which can be easily changed to
y = (4/5)x - 69/5 if need be.
To find the equation of a line parallel to a given line, we need to use two pieces of information: the given point and the fact that the line is parallel to the given line.
First of all, let's rearrange the given line equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:
4x - 5y = 8
-5y = -4x + 8
y = (4/5)x - 8/5
Since we want a line parallel to this given line, the parallel line will have the same slope. So, the slope of the line we are looking for is also 4/5.
Now that we have the slope (m = 4/5) and the point (6, -9), we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substituting in the values:
y - (-9) = (4/5)(x - 6)
y + 9 = (4/5)(x - 6)
To simplify, we can distribute (4/5) to (x - 6):
y + 9 = (4/5)x - (4/5) * 6
y + 9 = (4/5)x - 24/5
Finally, let's rearrange the equation to get it in the standard form Ax + By = C, where A, B, and C are integers:
5(y + 9) = 4x - 24
5y + 45 = 4x - 24
4x - 5y = 69
Therefore, the equation of the line containing the point (6, -9) and parallel to the line 4x - 5y = 8 is 4x - 5y = 69.