Question

Graph the line that passes through the points. Write its equation in slope- intercept form. (Review \(5.3 \text { for } 5.7)\) $$(14,-9),(-5,-3)$$

Short answer

The equation of the line in slope-intercept form that passes through the points (14,-9) and (-5,-3) is \(y = -\frac{6}{19}x - 6.26\).

Step-by-step solution

Calculate the Slope

The formula to calculate the slope (m) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Use the provided points \((14,-9)\) and \((-5,-3)\) to calculate the slope as: \(m = \frac{-3-(-9)}{-5-14} = \frac{6}{-19} = -\frac{6}{19}\).

Find the Y-Intercept

The slope-intercept form of a linear equation is \(y = mx + b\), where 'b' is the y-intercept. To find 'b', we will substitute one of the given points and the slope into the equation. If we substitute for \(x=14\) and \(y=-9\) we get \(-9 = -\frac{6}{19}*14 + b\). Solving for 'b', we get \(b = -9 + \frac{6}{19}*14 \approx -6.26\).

Write Equation in Slope-Intercept Form

Substituting the slope and the y-intercept into the formula, the equation becomes \(y = -\frac{6}{19}x - 6.26\).