Question

find the equation of the line passing through the points \\((-5,1)\\) and \\((5,7)\\).

\\y = \frac{?}{\quad}x + \quad\\

Explanation:

Calculate the slope of the line

We find the slope \(m\) using the coordinates \((-5, 1)\) and \((5, 7)\).

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 1}{5 - (-5)} = \frac{6}{10} = \frac{3}{5} $$

Find the y-intercept of the line

We use the slope-intercept form \(y = mx + b\) with the point \((5, 7)\).

$$ 7 = \frac{3}{5}(5) + b \implies 7 = 3 + b \implies b = 4 $$

Write the final equation

We substitute the slope and y-intercept back into the equation.

$$ y = \frac{3}{5}x + 4 $$

Answer:

Find the equation of the line passing through the points \((-5,1)\) and \((5,7)\).

\(y =\) <blank>\(\frac{3}{5}\)</blank>\(x +\) <blank>\(4\)</blank>