Question

I need help with 9-81 ASAP PLS THIS IS MY HW

Answer 1

To start, we know that the equation we are trying to find is a straight line. It hits the x-axis at -3 and the y-axis at -1.
Thus, we know that the line passes through (0, -1) and (-3, 0).

We can now find the gradient using the gradient form: $\frac{y_1 - y_2}{x_1 - x_2}$

Thus, the gradient becomes: $m = \frac{0 - (-1)}{-3 - 0}$
$m = -\frac{1}{3}$

Since we have a point of interest and a gradient, we can use the point-gradient form of a straight line to find the equation of the straight line.
$y - y_1 = m(x - x_1)$

Use either the y-intercept or the x-intercept as your point.
$y + 1 = -\frac{1}{3}(x - 0)$
$y + 1 = -\frac{1}{3}x$

Thus, the equation becomes:
$y = -\frac{1}{3}x - 1$

Now, since the shaded region is below the line, we know that the inequality becomes:

$y \leq -\frac{1}{3}x - 1$

But, since it's dotted, we need to exclude the line itself.
Thus, the inequality becomes:
$y < -\frac{1}{3}x - 1$

Answer 2

It is -72 lol. that's pretty basic you know