Exercise 36 Page 230

An equation in slope-intercept form follows a specific format. For an equation in this form, $m$ is the slope and $b$ is the $y\text{-}$intercept. Let's use the given points to calculate $m.$ We will start by substituting the points into the Slope Formula. A slope of $\frac{1}{6}$ means that for every $6$ horizontal steps in the positive direction, we take $1$ vertical step in the positive direction. Now that we know the slope, we can write a partial version of the equation. To complete the equation, we also need to determine the $y\text{-}$intercept, $b.$ Since we know that the given points will satisfy the equation, we can substitute one of them into the equation to solve for $b.$ Let's use $\left(\frac{5}{4},1\right).$ A $y\text{-}$intercept of $\frac{19}{24}$ means that the line crosses the $y\text{-}$axis at the point $\left(0,\frac{19}{24}\right).$ We can now complete the equation.