Question

If the slope of a straight line is 6 and if Y (the variable on the vertical axis) decreases by 60, then X (the variable on the horizontal axis):_______A) decreases by 600.B) increases by 10.C) increases by 600.D) decreases by 10.

Answer 1

Answer:

$\Delta x = \frac{-60}{6}=-10$

So then the correct answer on this case would be:

D) decreases by 10.

Explanation:

For this case we assume that we have a linear model given by this expression:

$y = mx+b$

Where m is the slope on this case m=6 and b the intercept.

So our model is given by: $y = 6x +b$

We want to see that if we decrease the value of y on 60 units what would be the change on the x axis.

Let's assume that we have two points $y_i = 6 x_i + b$ and $y_f = 6 x_f +b$

If we find the differences between those points we got:

$y_f - y_i = 6x_f +b -6x_i -b = 6 (x_f -x_i)$

And we can rewrite this like that:

$\Delta y = 6 \Delta x$

And if we know that $Delta y =-60$ then we can solve $\Delta x$ like this:

$\Delta x = \frac{-60}{6}=-10$

So then the correct answer on this case would be:

D) decreases by 10.