Question

A line passes through the point (6,13)
(
6
,
13
)
and has a slope of −2
−
2
. What is the equation of the line in slope-intercept form?(1 point)
y=
y
=
x+
x
+

Answer 1

To find the equation of a line in slope-intercept form (y = mx + b), where \( m \) is the slope and \( b \) is the y-intercept, we can use the point-slope form of the equation:

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

Given:
- The point \( (x_1, y_1) = (6, 13) \)
- The slope \( m = -2 \)

Substituting these values into the point-slope form:

\[
y - 13 = -2(x - 6)
\]

Now, simplify the equation:

\[
y - 13 = -2x + 12
\]

Next, add 13 to both sides to isolate \( y \):

\[
y = -2x + 12 + 13
\]

\[
y = -2x + 25
\]

So, the equation of the line in slope-intercept form is:

\[
y = -2x + 25
\]