Find the equation of the line which passes through the point (2,-3) and is parallel to the line 2x+y=6

1 answer

To find the equation of a line parallel to another line, we need to determine the slope of the given line and then use the point-slope form of a line.

First, let's rearrange the equation 2x + y = 6 into slope-intercept form (y = mx + b) by isolating y:
y = -2x + 6

From this equation, we can see that the slope of the given line is -2.
Since the line we are trying to find is parallel, it will also have a slope of -2.

Now we can use the point-slope form of a line, which is given by:
y - y1 = m(x - x1)

Plugging in the point (2,-3) and the slope (-2), we have:
y - (-3) = -2(x - 2)

Simplifying:
y + 3 = -2x + 4

Rearranging this equation to slope-intercept form:
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.