Questions: Find an equation in slope-intercept form for the line. Through (5,4) and (2,6) The equation of the line is

Solution Steps

To find the equation of a line in slope-intercept form (y = mx + b) that passes through two given points, we need to:

1. Calculate the slope (m) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
2. Use one of the points and the slope to solve for the y-intercept (b) using the formula \( y = mx + b \).

To find the slope \( m \) of the line passing through the points \((5, 4)\) and \((2, 6)\), we use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the given points: \[ m = \frac{6 - 4}{2 - 5} = \frac{2}{-3} = -\frac{2}{3} \]

Using the slope \( m = -\frac{2}{3} \) and one of the points, say \((5, 4)\), we can find the y-intercept \( b \) using the slope-intercept form \( y = mx + b \): \[ 4 = -\frac{2}{3} \cdot 5 + b \] \[ 4 = -\frac{10}{3} + b \] \[ b = 4 + \frac{10}{3} \] \[ b = \frac{12}{3} + \frac{10}{3} \] \[ b = \frac{22}{3} \]

Final Answer