Question

problem 22
19 write an equation in slope - intercept form for the line that passes through (-2, 5) and has a slope of - 1. (use of the set of axes below is optional.)
graph of a coordinate plane with grid lines
a.rei.b.3: solving linear inequalities (inequalities)
problem 23
41 which graph is the solution to the inequality 6.4 - 4x ≥ - 2.8?

1. number line with an open circle at 2.3 and arrow to the right, marked 2.1, 2.2, 2.3, 2.4, 2.5
2. number line with a closed circle at 2.3 and arrow to the right, marked 2.1, 2.2, 2.3, 2.4, 2.5
3. number line with an open circle at 2.3 and arrow to the left, marked 2.1, 2.2, 2.3, 2.4, 2.5
4. number line with a closed circle at 2.3 and arrow to the left, marked 2.1, 2.2, 2.3, 2.4, 2.5

problem 24
43 solve the inequality for y: 5(2 - y) > - 11y - 8

Explanation:

Problem 40

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $(x_1,y_1)=(-2,5)$ and $m=-3$.
$y - 5 = -3(x - (-2))$

Step2: Simplify the equation

Expand and rearrange to slope-intercept form $y=mx+b$.
$y - 5 = -3(x + 2)$
$y - 5 = -3x - 6$
$y = -3x - 6 + 5$

Step1: Isolate the variable term

Subtract 6.4 from both sides.
$6.4 - 4x - 6.4 \geq -2.8 - 6.4$
$-4x \geq -9.2$

Step2: Solve for x, reverse inequality

Divide by -4, flip the inequality sign.
$x \leq \frac{-9.2}{-4}$
$x \leq 2.3$

Step3: Match to number line

A closed dot at 2.3, arrow left.

Step1: Expand the left side

Distribute the 5 across the parentheses.
$5(2 - y) > -11y - 8$
$10 - 5y > -11y - 8$

Step2: Collect y terms on left

Add $11y$ to both sides.
$10 - 5y + 11y > -8$
$10 + 6y > -8$

Step3: Isolate the y term

Subtract 10 from both sides.
$6y > -8 - 10$
$6y > -18$

Step4: Solve for y

Divide both sides by 6.
$y > \frac{-18}{6}$

Answer:

$y = -3x - 1$

---

Problem 41