Question

Write an equation in point-slope form for the given line. Choose the correct answer below.





(1 point)
Responses

y=−2(x−4)
𝑦
=
−
2
(
𝑥
−
4
)
y is equal to negative 2 times open paren x minus 4 close paren

y−4=−2(x+4)
𝑦
−
4
=
−
2
(
𝑥
+
4
)
y minus 4 is equal to negative 2 times open paren x plus 4 close paren

y−4=−2(x−4)
𝑦
−
4
=
−
2
(
𝑥
−
4
)
y minus 4 is equal to negative 2 times open paren x minus 4 close paren

y=2(x+2)

Answer 1

To write an equation in point-slope form, we need a point on the line and the slope of the line.

The point-slope form is given by the equation:

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

where \( m \) is the slope, and \( (x_1, y_1) \) is a point on the line.

Let's analyze the given options briefly:

1. \( y = -2(x - 4) \) is in slope-intercept form and not point-slope.
2. \( y − 4 = -2(x + 4) \) has a point \( (-4, 4) \) and slope \( -2 \).
3. \( y − 4 = -2(x − 4) \) has a point \( (4, 4) \) and slope \( -2 \).
4. \( y = 2(x + 2) \) is also in slope-intercept form.

If the slope of the line is \( -2 \) and it passes through the point \( (4, 4) \), the correct point-slope form would be:

\[ y - 4 = -2(x - 4) \]

Thus, the correct answer is:

**\( y - 4 = -2(x - 4) \)**.