You have the following equation of two lines:
A) y = 2x + 1
B) 2x + y = 7
the general form of an equation of a line is given by:
y = mx + b
where m is the slope and b is the y-intercept.
The equation A is already written in the slope-intercep form. By comparing the equation with the general form you can notice that the slope is:
mA = 2
Next, you rewrite the equation B:
2x + y = 7 subtract 2x both sides
y = -2x + 7
by comparing with the general fom you have that the equation B has the following slope:
mB = -2
In order to determine if the lines are parallel,perpendicular, or neither, you calculate the quotien between the slopes of the lines.
mA/mB = 2/(-2) = -1
The quotient between the slopes is -1, this means that the lines are perpendicular
