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
+

1 answer

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:

\[ y = -2x + 25 \]