Question

Select the equation of a line, given a slope of -4 going through (-4,-8)

a
y=4x+3

b
y=-4x-8

c
y=4x+8

d
y=-4x+8

Answer 1

To find the equation of a line given a slope and a point, you can use the point-slope form of the equation of a line:

\[ y - y_1 = m(x - x_1) \]

where \( m \) is the slope and \((x_1, y_1)\) is the point the line passes through.

Here, the slope \( m \) is -4 and the point is (-4, -8).

Plugging in the values,

\[ y - (-8) = -4(x - (-4)) \]

This simplifies to:

\[ y + 8 = -4(x + 4) \]

Now, distribute the -4:

\[ y + 8 = -4x - 16 \]

Next, subtract 8 from both sides:

\[ y = -4x - 16 - 8 \]

\[ y = -4x - 24 \]

Now, we can check which of the given options matches our derived equation. None of the options directly show \( y = -4x - 24 \), which suggests a possible earlier error. However, let's examine the choices:

1. \( y = 4x + 3 \)
2. \( y = -4x - 8 \)
3. \( y = 4x + 8 \)
4. \( y = -4x + 8 \)

None of the provided choices match the equation \( y = -4x - 24 \) exactly.

So, none of the choices a, b, c, or d is correct based on the initial information given. Please check the slope and point once again to confirm.