write the equation of a line that contains point p = (2, 7) and is parallel to the line x-2y=6.
since it has slope 1/2,
y-7 = 1/2 (x-2)
Thanks so much
To find the equation of the line that is parallel to the given line, we need to use the same slope as the given line.
First, let's rearrange the given line, x - 2y = 6, to the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
x - 2y = 6
-2y = -x + 6
y = (1/2)x - 3
From the equation y = (1/2)x - 3, we can see that the slope of the given line is 1/2.
Since the line we need to find is parallel, it will have the same slope of 1/2.
Now, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of the given point.
Substituting the values of the given point P = (2, 7), and the slope m = 1/2 into the formula, we have:
y - 7 = (1/2)(x - 2)
Now, let's simplify the equation:
y - 7 = (1/2)x - 1
y = (1/2)x + 6
Therefore, the equation of the line that contains point P = (2, 7) and is parallel to the line x - 2y = 6 is y = (1/2)x + 6.
To find the equation of a line parallel to another line, we need to determine the slope.
The given line, x - 2y = 6, can be rewritten in slope-intercept form (y = mx + b) by isolating y:
x - 2y = 6
-2y = -x + 6
y = (1/2)x - 3
From the rewritten equation, we can see that the slope of the given line is 1/2.
Since the line we want to find is parallel, it will also have a slope of 1/2.
Using the point-slope form of a line (y - y1 = m(x - x1)), substituting the values of the point P(2, 7) and the slope 1/2:
y - 7 = (1/2)(x - 2)
Simplifying:
y - 7 = (1/2)x - 1
y = (1/2)x + 6
Therefore, the equation of the line parallel to x - 2y = 6 and passes through point P(2, 7) is y = 1/2x + 6.