Question

Graph the line that passes through the points. Write its equation in slope- intercept form. (Review \(5.3 \text { for } 5.7)\) $$(19,-2),(4,-1)$$

Short answer

The equation of the line in slope-intercept form is \(y = -\frac{1}{15}x - \frac{13}{15}\).

Step-by-step solution

Calculate the Slope

Use the slope formula, which is \(m = \frac{{y2 - y1}}{{x2 - x1}}\), to find the slope of the line. Substituting the given points (19, -2) and (4, -1), while considering \(x1 = 19\), \(y1 = -2\), \(x2 = 4\) and \(y2 = -1\), we get \(m = \frac{{-1 - (-2)}}{{4 - 19}} = \frac{1}{-15} = -\frac{1}{15}\).

Find the y-intercept

Use the slope and one of the given points in the slope-intercept equation \(y = mx + b\) to find the y-intercept \(b\). Calculate \(b\) by substituting \(m = -\frac{1}{15}\), \(x = 19\), and \(y = -2\) into the equation: \(-2 = -\frac{1}{15}(19) + b\). Solving for \(b\) gives \(b = -\frac{13}{15}\).

Write the Equation in Slope-Intercept Form

Substitute the values of the slope \(m = -\frac{1}{15}\) and the y-intercept \(b = -\frac{13}{15}\) into the slope-intercept form to get the equation of the line. The equation becomes \(y = -\frac{1}{15}x - \frac{13}{15}\).