Question

Graph the line that passes through the points. Write its equation in slope- intercept form. (Review \(5.3 \text { for } 5.7)\) $$(6,-2),(-5,-8)$$

Short answer

The equation of the line in slope-intercept form is \(y = \frac{6}{11}x - \frac{58}{11}\).

Step-by-step solution

Finding the slope

First find the slope of the line passing through given points (6,-2) and (-5,-8). The slope \(m\) is given by: \[m = \frac{y_2 - y_1}{x_2 - x_1}\] So, plug the coordinates of the given points: \[m = \frac{-8 - (-2)}{-5 - 6} = \frac{-6}{-11} = \frac{6}{11}\]

Writing the point-slope form of the equation

The point-slope form of the line equation is given by: \[y - y_1 = m(x - x_1)\] Substitute the values of one of the points and the slope into the equation: \[y - (-2) = \frac{6}{11}(x - 6)\]

Converting to slope-intercept form

The slope-intercept form of the line equation is \(y = mx + b\). So, simplify the equation obtained in step 2 to get it in the slope-intercept form: \[y + 2 = \frac{6}{11}x - \frac{36}{11}\] \[y = \frac{6}{11}x - \frac{36}{11} - 2\] \[y = \frac{6}{11}x - \frac{58}{11}\]