Questions: Find the equation of the line passing through the points (-5,1) and (3,3).

Solution Steps

To find the equation of the line passing through two points, we can use the point-slope form of a line equation. First, calculate the slope (m) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Then, use one of the points and the slope to write the equation in the point-slope form \( y - y_1 = m(x - x_1) \). Finally, convert it to the slope-intercept form \( y = mx + b \).

To find the equation of the line passing through the points \((-5, 1)\) and \((3, 3)\), we first calculate the slope \(m\) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 1}{3 - (-5)} = \frac{2}{8} = 0.25 \]

Using the slope \(m = 0.25\) and one of the points, say \((-5, 1)\), we can find the y-intercept \(b\) using the point-slope form: \[ y - y_1 = m(x - x_1) \] Substituting the values, we have: \[ 1 - 1 = 0.25(-5 - (-5)) \] Simplifying, we find: \[ b = 1 - 0.25 \times (-5) = 1 + 1.25 = 2.25 \]

Now that we have both the slope \(m = 0.25\) and the y-intercept \(b = 2.25\), we can write the equation of the line in slope-intercept form: \[ y = 0.25x + 2.25 \]

Final Answer