Question

writing the equation of a line in slope-intercept form given two points

write the equation of the line that passes through the points \\((-1, 2)\\) and \\((6, 3)\\) in slope-intercept form.

step 1: choose \\((x_1, y_1)\\).

Explanation:

Identify the given points and target

We are given two points on a line: \((-1, 2)\) and \((6, 3)\). The goal is to write the equation of this line in slope-intercept form, which is \(y = mx + b\). The first step shown in the interactive interface is to choose \((x_1, y_1)\) from the given points.

Select the first point

Using the Slope Formula knowledge point

$$ (x_1, y_1) = (-1, 2) $$

Calculate the slope of the line

Using the Slope Formula knowledge point

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 2}{6 - (-1)} = \frac{1}{7} $$

Write the equation in slope-intercept form

Using the Slope-Intercept Form knowledge point

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Answer:

Write the equation of the line that passes through the points \((-1, 2)\) and \((6, 3)\) in slope-intercept form.

Step 1: Choose \((x_1, y_1)\). <blank>\((-1, 2)\)</blank>