Find the equation of the line that contains the point (3, 2) and is parallel to the line 3x − 9y = 0.
I know I solve for y and I get y= -3x/-9 but I am not sure where to go from here please help.
find slope in second line
y=1/3 x so slope is 1/3
new line
y=1/3 x + b
put in 3,2, and solve for b.
To find the equation of a line parallel to another line, you need to use the fact that parallel lines have the same slope.
First, let's rewrite the given line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Start by isolating y on one side of the equation:
3x − 9y = 0
-9y = -3x
Divide by -9 to solve for y:
y = (-3x)/(-9)
Simplify:
y = (1/3)x
From this equation, we can see that the slope of the given line is 1/3.
Now, we want to find the equation of a line that is parallel to this line and passes through the point (3, 2).
Since parallel lines have the same slope, we can use the slope-intercept form (y = mx + b) and substitute the slope and the coordinates of the point (3, 2) into the equation. This will give us the value of the y-intercept, b.
Using the point-slope form:
y - y1 = m(x - x1)
Substitute (3, 2) as (x1, y1) and 1/3 as the slope m:
y - 2 = (1/3)(x - 3)
Now, let's simplify this equation:
y - 2 = (1/3)x - 1
y = (1/3)x + 1
Therefore, the equation of the line parallel to 3x − 9y = 0 and passing through the point (3, 2) is y = (1/3)x + 1.