Question

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

Answer 1

To find the equation of a line in slope-intercept form (y = mx + b), you need the slope (m) and the y-intercept (b).

You've mentioned that the slope (m) is -2 and that the line passes through the point (6, 13).

We can use the point-slope form of the equation of a line, which is:

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

where \( (x_1, y_1) \) is the point on the line. Plugging in the values:

- \( m = -2 \)
- \( x_1 = 6 \)
- \( y_1 = 13 \)

The equation becomes:

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

Now, we'll simplify the equation:

1. Distribute the slope (-2):
\[
y - 13 = -2x + 12
\]

2. 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:

\[
y = -2x + 25
\]

Thus, your final answer is:
\[
y = -2x + 25
\]