Question

which graph represents the equation $y = -\frac{4}{3}x - 27$
a

b

c

c
b
a
no answer text provided.
question 1 pts
which line passes through the points (-4, -0.25) and (1.8, -3.15)?
a. $y = 0.5x + 2.25$ \t\tc. $y = -2x - 7.75$
b. $y = -0.5x - 2.25$ \t\td. $y = 2x + 7.75$

Explanation:

Step1: Calculate the slope

The slope \( m \) between points \((x_1, y_1) = (-4, -0.25)\) and \((x_2, y_2) = (1.8, -3.15)\) is:
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3.15 - (-0.25)}{1.8 - (-4)} = \frac{-2.9}{5.8} = -0.5$$

Step2: Find the y-intercept

Use point-slope form \( y - y_1 = m(x - x_1) \) with \( m = -0.5 \) and \((-4, -0.25)\):
$$y - (-0.25) = -0.5(x - (-4))$$
Simplify:
$$y + 0.25 = -0.5x - 2$$
$$y = -0.5x - 2.25$$

Step3: Verify the equation

Check if the second point \((1.8, -3.15)\) satisfies \( y = -0.5x - 2.25 \):
$$y = -0.5(1.8) - 2.25 = -0.9 - 2.25 = -3.15$$
It matches, so the equation is correct.

Answer:

B. y = -0.5x - 2.25