Find an equation of the line that passes through the point (3,10) and is parallel to the line x-3y=1
since it is parallel, the new equation should also start off with
x - 3y = ????
so let x -3y = c
sub in the point
3 - 3(10) = c
c = -27
so x - 3y = -27
Oh, parallel lines, eh? They never seem to meet, do they? Anyway, let's get down to business.
To find the equation of a line that is parallel to another line, we need to have the same slope. So let's find the slope of the given line, x - 3y = 1.
If we rearrange the equation to slope-intercept form (y = mx + b), we can easily determine the slope (m). Let's do that:
x - 3y = 1
-3y = -x + 1
y = (1/3)x - 1/3
Ah, so the slope of the original line is 1/3. Therefore, the parallel line will also have a slope of 1/3.
Now, we have the slope and a point on the line (3, 10). We can use the point-slope form of a line to write the equation:
y - y1 = m(x - x1)
Plugging in the values, we get:
y - 10 = (1/3)(x - 3)
And if we simplify this equation, we get:
y - 10 = (1/3)x - 1
So the equation of the line parallel to x - 3y = 1 and passing through the point (3, 10) is:
y = (1/3)x + 9
Voila! Now you have an equation to parallel your thoughts.
To find the equation of a line that is parallel to another line, we need to determine the slope of the given line first. The equation of the given line is x - 3y = 1.
Let's rearrange the equation in the slope-intercept form y = mx + b, where m represents the slope and b represents the y-intercept.
x -3y = 1
-3y = -x + 1
y = (1/3)x - 1/3
From this equation, we can see that the slope of the given line is 1/3.
Since the line we want to find is parallel to the given line, it will have the same slope of 1/3.
Now, we have the slope (m = 1/3) and a point (3, 10) that the line passes through.
We can use the point-slope form y - y1 = m(x - x1) to find the equation of the line.
Plugging in the values:
y - 10 = (1/3)(x - 3)
Now, let's simplify the equation:
y - 10 = (1/3)x - 1
Adding 10 to both sides:
y = (1/3)x + 9
Thus, the equation of the line that passes through the point (3, 10) and is parallel to the line x - 3y = 1 is y = (1/3)x + 9.
To find the equation of a line parallel to the line x - 3y = 1, we need to determine the slope of the given line.
The equation x - 3y = 1 can be rewritten in slope-intercept form, y = mx + b, by solving for y:
-3y = -x + 1
y = (1/3)x - 1/3
From the equation, we can see that the slope (m) of the given line is (1/3).
Since the line we want is parallel to this line, it will have the same slope. So, the slope of the line we're looking for is also (1/3).
Now that we have the slope, we can use the point-slope form of the equation of a line to write the equation. The point-slope form is: y - y₁ = m(x - x₁), where (x₁, y₁) represents the coordinates of a point on the line.
Given that the line passes through the point (3,10), we substitute these values into the point-slope form:
y - 10 = (1/3)(x - 3)
Expanding the equation:
y - 10 = (1/3)x - 1
Now, we'll rearrange the equation to isolate y:
y = (1/3)x - 1 + 10
y = (1/3)x + 9
Therefore, the equation of the line that passes through the point (3,10) and is parallel to the line x - 3y = 1 is y = (1/3)x + 9.