Hey can someone help, this is a true or false

Question

The line x=-1 and passes through (3,-4) is perpendicular to y=1x-4

True or false?

Answer 1

First look at each equation individually.

x = -1 is in the form of x = a, which means it has no y- intercept and can only be parallel to the y-axis.

y = 1x - 4 has a slope of 1/1 therefore it cannot be perpendicular to a line which is vertical. A line that was perpendicular to x = -1 would have the form of y = b

Therefore, the statement is false.

Answer 2

Maybe you meant to write

y=-1x -1 or x=-1y - 1 is a line through the point (3,-4) and perpendicular to y=1x-4

then it would be true.

It's a little unusual to write 1x as the 1 is implicit and understood without writing it.

so it's suspicious when you write x=-1, as maybe you also intended it to go with y as x=-1y. or maybe y=-1x

to be perpendicular, the coefficient of the x term must be a negative inverse. If y=x-4 is one line, the perpendicular line would have -1 as the coefficient of x, when the equations are solved for y.

the point (3,-4) has a y coordinate the same as the y intercept of the line y=x-4

y=-x + b with b = any number is perpendicular to y=x-4, but to go through (3,-4) plug in the number and solve for b

-4 =-3+b

b =-4+3 = -1

the perpendicular line through the given point is y=-x-1 or in your way of writing, it would be y=-1x-1, which is also the same as x=-1y-1. Which makes it suspicious that you had a typo in the problem or mis-copied it?