What is the slope of a line that is perpendicular to the line that passes through (1,0) and is parallel to y=3x+5

Slope is perpendicular to the line that passes (1, 0) & is parallel to y = 3x + 5

We need to first find the slope. Since we're already given an equation, we can simply find it within there :)

We're given an equation in slope intercept form (y = mx + b) so we can simply look in the "m" spot. Therefore, we know that the slope is 3.

Since our slope is perpendicular to the given line, we must find the negative reciprocal of the slope.

A negative reciprocal is simply a number flipped over and then given a negative (or a negative is removed).

An example is here : slope = 8 → negative reciprocal of slope = -1/8

So, our negative reciprocal of "3" is -1/3.

Therefore, our new slope is -1/3.

Now, since it passes through (1, 0) then this is how we are going to find out y-intercept to input it into our new equation.

y = mx + b

Simply plug in everything (including slope and y)

0 = (-1/3)(1) + b

Simplify.

0 = -1/3 + b

Add 1/3 to both sides.

1/3 = b

Therefore, our y-intercept is b.

Now that we have all of the needed variables for our new equation, simply plug everything into an all new equation :)

y = mx + b

y = -1/3x + 1/3

~Hope I helped!~