What is the equation of the line that passes through the points (−3,4)

and (−6,3)
? Write the answer in slope-intercept form.(1 point)
y=
(
)x+

1 answer

To find the equation of the line that passes through the points \((-3, 4)\) and \((-6, 3)\), we need to determine the slope and then use the point-slope form of a line.

  1. Calculate the slope (m):

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Plugging in our points:

  • \((x_1, y_1) = (-3, 4)\)
  • \((x_2, y_2) = (-6, 3)\)

\[ m = \frac{3 - 4}{-6 - (-3)} = \frac{-1}{-6 + 3} = \frac{-1}{-3} = \frac{1}{3} \]

  1. Use the point-slope form to find the equation:

The point-slope form of the equation of a line is given by:

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

Using the slope \(m = \frac{1}{3}\) and the point \((-3, 4)\):

\[ y - 4 = \frac{1}{3}(x + 3) \]

  1. Convert to slope-intercept form (y = mx + b):

First, distribute on the right side:

\[ y - 4 = \frac{1}{3}x + 1 \]

Now, add 4 to both sides:

\[ y = \frac{1}{3}x + 1 + 4 \] \[ y = \frac{1}{3}x + 5 \]

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

\[ \boxed{y = \frac{1}{3}x + 5} \]

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