Find the equation of the line which passes through the point (2,-3) and is parallel to the line 2x+y=6
To find the equation of the line that is parallel to 2x+y=6, we need to determine its slope.
The given line is in the form of "y = mx + b" where m is the slope. So, to find the slope, we need to rearrange the equation in this form.
Starting with 2x + y = 6, subtracting 2x from both sides gives us y = -2x + 6.
Now, we can see that the slope of the given line is -2.
Since a line parallel to the given line will have the same slope, the slope of the new line is also -2.
We know that the line passes through the point (2, -3).
We can now use the point-slope form to find the equation of the line.
The point-slope form is: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
Plugging in the values, we get:
y - (-3) = -2(x - 2)
Simplifying, we have:
y + 3 = -2x + 4
Subtracting 3 from both sides gives us:
y = -2x + 1
So, the equation of the line that passes through the point (2, -3) and is parallel to the line 2x + y = 6 is y = -2x + 1.
To find the equation of a line parallel to the given line, we need to determine the slope of the given line.
The equation of the given line is 2x + y = 6. To convert this equation to slope-intercept form (y = mx + b), where m is the slope, we can isolate y:
y = -2x + 6
From this equation, we can see that the slope of the given line is -2.
Since a line parallel to the given line will have the same slope, the slope of the line we want to find is also -2.
We also have a point on the line we want to find, which is (2, -3).
Using the point-slope form of a line, we can write the equation as:
y - y1 = m(x - x1)
Where (x1, y1) is the given point and m is the slope. Plugging in the values:
y - (-3) = -2(x - 2)
Simplifying:
y + 3 = -2x + 4
Rearranging the equation to isolate y:
y = -2x + 1
Therefore, the equation of the line that passes through the point (2, -3) and is parallel to the line 2x + y = 6 is y = -2x + 1.