WRITING AN EQUATION Write an equation in slope-intercept form of the line that passes through the given points. \( \begin{array}{lll}\text { 14. }(-1,-1),(1,5) & \text { 15. }(2,4),(3,6) & \text { 16. }(-2,3),(2,7) \\ \text { 17. }(4,1),(8,2) & \text { 18. }(-9,5),(-3,3) & \text { 19. }(1,2),(-2,-1)\end{array} \)

To write the equation in slope-intercept form \(y = mx + b\), start by finding the slope \(m\) using the formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\). For example, for points (-1, -1) and (1, 5), the slope is \(m = \frac{5 - (-1)}{1 - (-1)} = \frac{6}{2} = 3\). Now, choose one point, like (-1, -1). Plug it into the equation: \(-1 = 3(-1) + b\) to find \(b\). Solving this gives you \(b = 2\). Therefore, the equation is \(y = 3x + 2\). For point pairs like (2, 4) and (3, 6), you’ll notice that they are closely linked. The slope also turns out to be \(m = \frac{6 - 4}{3 - 2} = 2\). Using the point (2, 4), substitute into the equation: \(4 = 2(2) + b\), leading to \(b = 0\). The final equation here is \(y = 2x\). This method works for all pairs you listed!