For the equation, y = −x − 4, tell whether its graph passes through the first quadrant. explain how you know.

no; for x > 0 the y-values are negative.

yes; for x > 0 some y-values are positive.

yes; for x < 0 some y-values are positive.

no; for x < 0 the y-values are negative

Option 1

No; for x > 0 the y-values are negative.

The given line equation will not pass through 1st quadrant. So option 1 is correct. As for x > 0, the y – values are positive

Given that, an equation is y = - x – 4  

We have to find whether the given line equation will passes through the 1st quadrant or not.

Now, we know that, in 1st quadrant both the values of x and y will be positive.

So, now if we observe. For any positive value of x in y = - x – 4 the y value will always be negative. Because of the (-) symbol before it.

So, no value y will be positive for a positive value of x. and even the vice versa is not possible.

Hence, the given line equation will not pass through 1st quadrant. So option 1 is correct. As for x > 0 , the y – values are positive.