Step-by-step explanation:
first let's get the original line in slope intercept form.
the vegetal slope intercept form is
y = ax + b
a is the slope, b is the y-intercept.
2x + y = 5
y = -2x + 5
there !
a line parallel to this line must have the same slope (-2).
but it will intersect with the y-axis at a different point.
the y-intersect is the y value when x = 0.
the given point (0, 1) is already that y-intersect (because x=0).
so, the desired parallel line function is
y = -2x + 1
if we had a different point of the line, e.g. (4, -7), we would go back to the general equation
y = ax + b
put in the slope we know (-2)
y = -2x + b
and then put in the x and y cakes if the point and calculate b
-7 = -2×4 + b
-7 = -8 + b
b = 1
and then we get again
y = -2x + 1
.
