WRITING AN EQUATION Write an equation in slope-intercept form of the line that passes through the given points. \( \begin{array}{lll}\text { 14. }(-1,-1),(1,5) & \text { 15. }(2,4),(3,6) & \text { 16. }(-2,3),(2,7) \\ \text { 17. }(4,1),(8,2) & \text { 18. }(-9,5),(-3,3) & \text { 19. }(1,2),(-2,-1)\end{array} \)
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To find the equation in slope-intercept form \(y = mx + b\), you start by calculating the slope \(m\). Use the formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\). For example, with the points (-1, -1) and (1, 5), slope \(m\) is \(\frac{5 - (-1)}{1 - (-1)} = \frac{6}{2} = 3\). Next, use one of the points in the slope-intercept formula to find \(b\), the y-intercept. For point (1, 5): \(5 = 3(1) + b\) leads to \(b = 2\). So, the final equation is \(y = 3x + 2\). Now let's tackle the second pair, (2, 4) and (3, 6). The slope here is \(m = \frac{6 - 4}{3 - 2} = 2\). Using point (2, 4) gives you \(4 = 2(2) + b\), so \(b = 0\). The equation is \(y = 2x\). Repeat this process for the remaining points to get more equations!
