write an equation for the line. The first point is at (-5, 0) and the second point is at (4, 3)

Answer 1

To find the equation of the line that passes through the points \((-5, 0)\) and \((4, 3)\), we can follow these steps:

1. Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting in the coordinates:

   • \( (x_1, y_1) = (-5, 0) \)
   • \( (x_2, y_2) = (4, 3) \)

   \[ m = \frac{3 - 0}{4 - (-5)} = \frac{3}{4 + 5} = \frac{3}{9} = \frac{1}{3} \]

2. Use the point-slope form of the line: \[ y - y_1 = m(x - x_1) \] Substituting one of the points (let's use \((-5, 0)\)) and the slope \(m = \frac{1}{3}\): \[ y - 0 = \frac{1}{3}(x - (-5)) \] Simplifying: \[ y = \frac{1}{3}(x + 5) \]

3. Convert to slope-intercept form (y = mx + b): \[ y = \frac{1}{3}x + \frac{5}{3} \]

The equation of the line is: \[ y = \frac{1}{3}x + \frac{5}{3} \]