Point Line
(−7, 6) x + y = 3
Write an equation of the line through the point parallel to the given line.
How do I start this
see the question below (probably also posted by you). You have a point and a slope (that of the parallel line), so ...
what is the slope of x+y = 3 ?
y = -1 x + 3
slope = -1
so I need a line of form
y = -1 x + b that goes through (-7,6)
6 = 7 + b
b = -1
so
y = -1 x -1
or
x+y = -1
y=-1x-1
and then y=1x+13
Those are my answers
y = 1 x + 13 has slope of +1
It is not parallel to x+y = 3 which has slope of -1
It is in fact perpendicular.
Sorry that is what I meant.
Y=-1x-1 is my parallel and the y=1x+13 is perpendicular
To find the equation of a line parallel to a given line, we need to remember that parallel lines have the same slope.
Here's how you can start:
1. Identify the slope of the given line. The equation of the given line is in the form "Ax + By = C" or "y = mx + b", where m represents the slope. In this case, the given line is "x + y = 3".
To find the slope in this case, rearrange the equation to the slope-intercept form "y = mx + b" by isolating y. Subtract x from both sides:
y = -x + 3
So, the slope of the given line is -1.
2. Since the line we're looking for is parallel to the given line, it will have the same slope of -1.
3. Use the point-slope form of the equation 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.
Let's use the point (-7, 6) and the slope -1 to write the equation:
y - 6 = -1(x - (-7))
Simplifying,
y - 6 = -1(x + 7)
Now, we can expand the equation:
y - 6 = -x - 7
Add 6 to both sides to isolate y:
y = -x - 1
Hence, the equation of the line parallel to "x + y = 3" and passing through the point (-7, 6) is "y = -x - 1".