A line passes through the points (6,10)

Question

(
6
,
10
)
and (18,6)
(
18
,
6
)
. What is the equation of the line in slope-intercept form?(1 point)
Responses

y=−13x+12
y
=
−
1
3
x
+
12
y equals negative Start Fraction 1 over 3 End Fraction x plus 12

y=−3x+12
y
=
−
3
x
+
12
y equals negative 3 x plus 12

y=3x+6
y
=
3
x
+
6
y equals 3 x plus 6

y=13x+6

Answer 1

To find the equation of the line that passes through the points (6,10) and (18,6), we first need to calculate the slope (m) of the line using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Where \((x_1, y_1) = (6, 10)\) and \((x_2, y_2) = (18, 6)\).

Plugging in the values:

\[ m = \frac{6 - 10}{18 - 6} = \frac{-4}{12} = -\frac{1}{3} \]

Now that we have the slope, we can use the point-slope form of a line, which is:

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

Using the point (6, 10) and the slope \(m = -\frac{1}{3}\):

\[ y - 10 = -\frac{1}{3}(x - 6) \]

Now, distribute the slope on the right side:

\[ y - 10 = -\frac{1}{3}x + 2 \]

Next, add 10 to both sides to solve for \(y\):

\[ y = -\frac{1}{3}x + 2 + 10 \] \[ y = -\frac{1}{3}x + 12 \]

The equation of the line in slope-intercept form is:

\[ y = -\frac{1}{3}x + 12 \]

Therefore, the correct response is:

y = −(1/3)x + 12 (which matches the format of some of your options)