Write an equation of the line containing The given point in parallel to the given line (9,-9);4x-7y=5
4x-7y=5
7 y = 4 x - 5
y = (4/7) x - 5/7
so the slope is 4/7
the parallel line has the same slope so
y = (4/7) x + b
-9 = (4/7) 9 + b
b = -9 -9(4/7)
b = -9 (1 + 4/7) = -9(11/7) = -99/7
so
y = (4/7) x -99/7
7 y = 4 x -99
Easiest way:
Since the slopes are the same, the equations differ only in the constant
New equation is
4x - 7y = c, plug in the given point (9, -9)
36 + 63 = c = 96
new equation: 4x - 7y = 99
To find the equation of a line parallel to the given line, we need to determine the slope of the given line.
Given line: 4x - 7y = 5
To express this equation in slope-intercept form (y = mx + b), we solve for y:
-7y = -4x + 5
y = (4/7)x - (5/7)
The slope of the given line is m = 4/7.
Since the line we are looking for is parallel to the given line, it will have the same slope.
Using the point (9, -9) and the slope 4/7, we can write the equation of the parallel line.
y - y1 = m(x - x1)
y - (-9) = (4/7)(x - 9)
y + 9 = (4/7)(x - 9)
This is the equation of the line containing the point (9, -9) and parallel to the given line, 4x - 7y = 5.
To find the equation of a line parallel to a given line, we need to determine the slope of the given line first. The slope of a line is determined by the coefficient of x when the equation is in the form y = mx + b, where m is the slope.
Given line: 4x - 7y = 5
To get the equation in slope-intercept form, we isolate y:
-7y = -4x + 5
Dividing by -7:
y = (4/7)x - 5/7
Now, we can find the slope of the given line, which is (4/7).
Since the line we are looking for is parallel to the given line, it will have the same slope. So, the equation of the line parallel to the given line will be:
y = (4/7)x + b
To find the value of b, we can substitute the coordinates of the given point (9, -9) into the equation:
-9 = (4/7)(9) + b
Simplifying:
-9 = 36/7 + b
To isolate b, we can subtract 36/7 from both sides:
b = -9 - 36/7
b = (-63 - 36)/7
b = -99/7
Therefore, the equation of the line containing the point (9, -9) and parallel to the line 4x - 7y = 5 is:
y = (4/7)x - 99/7