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m_a_m_a [10]
3 years ago
6

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

Mathematics
2 answers:
nalin [4]3 years ago
5 0
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
Yuri [45]3 years ago
4 0
It is -72 lol. that's pretty basic you know
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