Question

Write an equation of the line containing the given point and parallel to the given line.
​(9​, -9​); 9x - 2y = 5

Answer 1

To find the equation of a line parallel to another line, we need to know that parallel lines have the same slope.

First, we need to find the slope of the given line. We can rewrite the equation 9x - 2y = 5 in slope-intercept form (y = mx + b) to make it easier to identify the slope.

Starting with 9x - 2y = 5:
-2y = -9x + 5
Dividing by -2:
y = 9/2x - 5/2

So, the slope of the given line is 9/2.

Since the line we want is parallel to the given line, it will also have a slope of 9/2.

We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)

Plugging in the values:
y - (-9) = 9/2(x - 9)

Simplifying:
y + 9 = 9/2(x - 9)

Now we can distribute the 9/2:
y + 9 = 9/2x - 9(9/2)

Simplifying again:
y + 9 = 9/2x - 81/2

To get rid of the fraction, we can multiply everything by 2:
2(y + 9) = 2(9/2x - 81/2)

Distributing:
2y + 18 = 9x - 81

Now, let's rearrange the equation to get it in standard form:
-9x + 2y = -99

So, the equation of the line containing the point (9, -9) and parallel to the line 9x - 2y = 5 is -9x + 2y = -99.