Question 124234
First, you want to write the new equation in the "slope-intercept" form (y = mx+b) unless instructed otherwise.
Second, recall that parallel lines have identical slopes, so if you know the slope of the line whose equation is given (y = -x+3), then you autmatically know the slope of any line parallel to this.
Compare the given equation which is already in the slope-intercept form with the general form:
y = -x+3
y = mx+b
You can see that the slope, m, of the given equation is -1.
So the slope of the new equation will be -1 because the new line is parallel to the given line.
Ok, now you can write the slope (m = -1) into the general equation:
y = -x+b
Now you need to find the value of b, the y-intercept.
You do this by substituting the x and y of the above equation with the x and y values taken from the given point (2, 4) through which the new line passes.
y = -x+b Substitute x = 2 and y = 4
4 = -2+b Add 2 to both sides.
6 = b This is the y-intercept of the new line so now you can write the final equation:
y = -x+6
I hope this clarifies the problem for you!