Question

Help Meh PleAse: Fill in the blanks

Answer 1

$\sf2x+3y=-9$

Convert to slope-intercept form, y = mx + b.

$\sf2x+3y=-9$

Subtract 2x to both sides:

$\sf3y=-2x-9$

Divide 3 to both sides:

$\sf~y=-\dfrac{2}{3}x-3$

Now it's in slope intercept form, y = mx + b where 'm' is the slope. So the slope here is -2/3, which is Negative.

$\sf~y=3x-6$

This is already in slope intercept form. So the slope here is 3, which is Positive.

For #3 and #4, take any two points from the table and plug them into the slope formula.

$\sf~m=\dfrac{y_2-y_1}{x_2-x_1}$

Let's take (0, 7) and (1, 5).
               x1 y1       x2 y2

$\sf~m=\dfrac{5-7}{1-0}$

Subtract:

$\sf~m=\dfrac{-2}{1}$

Divide:

$\sf~m=-2$

So the slope is negative.

For #4, let's take (2, -8) and (3, -7)
                         x1  y1       x2  y2

$\sf~m=\dfrac{-7-(-8)}{3-2}$

Subtract:

$\sf~m=\dfrac{1}{1}$

Divide:

$\sf~m=1$

So the slope is positive.