Write an equation of the line that is parallel to the line y= -x+4 and passes through the point (0,10).
m' = -1/(-1) = 1 = new slope
y = x + b
10 = 0 + b
b = 10
so
y = x + 10
To find the equation of a line that is parallel to another line, we need to know that parallel lines have the same slope. In this case, the given line has a slope of -1.
The slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept. Since the line is parallel to y = -x + 4, it means it has the same slope, which is -1.
Now we can substitute the slope (-1) and the given point (0,10) into the slope-intercept form and solve for the y-intercept (b):
10 = -1(0) + b
10 = 0 + b
b = 10
So the equation of the line parallel to y = -x + 4 and passing through (0,10) is y = -x + 10.