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 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.
To find the equation of a line parallel to the given line, we need to determine the slope of the given line first. The equation 2x + y = 6 is in the standard form, which is y = mx + b, where m represents the slope of the line.
To determine the slope, we need to rearrange the given equation in slope-intercept form, y = mx + b. Let's solve for y:
2x + y = 6
y = -2x + 6
Comparing this with the slope-intercept form, we can determine that the slope, m, of the given line is -2.
Since the line we need to find is parallel to this line, it will also have a slope of -2.
Now, we have the slope and a point on the line (2, -3). We can use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), to find the equation.
Let's substitute the values into the point-slope form:
y - (-3) = -2(x - 2)
Simplifying:
y + 3 = -2x + 4
Rearranging the equation:
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.