write an equation of the line containing the given point and parallel to the given line.
(5,-8); 9x-5y=2
put the equation in slope intercept form. A line parallel will have the same slope.
9x-5y = 2; y = 9/5x -(2/5)
(using y=mx+c)
Slope of the given line = 9/5
hence the required line will have the same slope(9/5) since it is parallel.
Now putting the given point(5,-8)in y=mx+c; since it passes through (5,-8)
-8 = m * 5 + c where m= slope = 9/5
or -8 = (9/5)*5 + c
or c = -8-9; c = -17
Equation of the required line is
y = 9/5 x + (-17)
or 5y = 9x - 85
or 9x - 5y = 85 is the answer
To find the equation of a line parallel to the given line, we need to use the fact that parallel lines have the same slope.
The given line has the equation: 9x - 5y = 2
Let's rearrange this equation in slope-intercept form, y = mx + b, where m is the slope:
-5y = -9x + 2
y = (9/5)x - 2/5
The slope of the given line is (9/5).
Since the parallel line we want to find should have the same slope, its equation will also have a slope of (9/5).
Now, we have the point the line passes through: (5, -8). We will use this point to find the y-intercept (b) of the line.
The equation for the line can be written as:
y = mx + b
Substituting the values of the point (5, -8):
-8 = (9/5)(5) + b
-8 = 9 + b
b = -17
So, the equation of the line parallel to 9x - 5y = 2 and passing through the point (5, -8) is:
y = (9/5)x - 17