Write an equation of the line passing through \( (-2,3) \) and \( (6,4) \). Give the answer in standard form. The equation of the line in standard form is

To find the equation of the line passing through the points \( (-2,3) \) and \( (6,4) \), we first need to calculate the slope \( m \). The slope is given by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 3}{6 - (-2)} = \frac{1}{8} \] Now, we can use the point-slope form of a line equation, which is \( y - y_1 = m(x - x_1) \). Using point \( (-2, 3) \): \[ y - 3 = \frac{1}{8}(x + 2) \] Now, we simplify and put it in standard form \( Ax + By = C \): \[ y - 3 = \frac{1}{8}x + \frac{1}{4} \] \[ y = \frac{1}{8}x + \frac{1}{4} + 3 \] \[ y = \frac{1}{8}x + \frac{13}{4} \] To eliminate the fraction, multiply through by 8: \[ 8y = x + 26 \] \[ -x + 8y = 26 \] Rearranging gives the equation in standard form: \[ -x + 8y = 26 \] So, the equation of the line in standard form is: \[ x - 8y = -26 \]