Question

# Find the equation of a line with slope $- 1$ and cutting off an intercept of 4 units on the negative direction of the y-axis.

Hint: Here we use the slope form of a given line which is $y = mx + c$. Then we try to find the equation of the line using the given values of m and c.

Given, a line with slope $- 1$, so, we have, slope (m) $= - 1$
And it is cutting off an intercept of 4 units on the negative direction of the y-axis.
So, we have, as per, the slope form of the a line,$y = mx + c$, here, $c = - 4$,
Then, we have the equation of line as, $y = mx + c$ and $c = - 4$,$m = - 1$,
On substituting the values we get,
$y = ( - 1)x + ( - 4)$
$\Rightarrow y = - x - 4$
$\Rightarrow y + x + 4 = 0$
This is our desired equation of the line.

Note: The equation of a straight line in the slope form is given by $y = mx + c$ where m is the slope and c is a desired constant. Here in this problem, as it is cutting off an intercept of 4 units on negative direction of y-axis, for, $x = 0,$we must have, $y = - 4$. And that is what we are getting from our answer. So we can check that our answer is correct.