Learn with an example Rewrite the following equation in slope-intercept form. \[ y-10=\frac{1}{4}(x+4) \] Write your answer using integers, proper fractions, and impro,

First, let's start by simplifying the given equation: \[ y - 10 = \frac{1}{4}(x + 4) \] To isolate \(y\), you would distribute \(\frac{1}{4}\) across the bracket: \[ y - 10 = \frac{1}{4}x + 1 \] Next, add 10 to both sides to solve for \(y\): \[ y = \frac{1}{4}x + 11 \] And there you have it! In slope-intercept form, the equation is: \[ y = \frac{1}{4}x + 11 \] Now, let’s talk about how this form helps you. The slope-intercept form, \(y = mx + b\), makes it super easy to identify the slope (m) and the y-intercept (b). Here, the slope of \(\frac{1}{4}\) tells you that for every 4 units you move right on the x-axis, you move 1 unit up on the y-axis. This gentle slope indicates a gradual rise. Another fun fact is that this form allows for quick graph plotting! With the y-intercept at 11, you can plot your starting point on the y-axis, then use the slope to find more points. For instance, starting at (0, 11) and following the slope would take you to (4, 12) and then (8, 13). Voila, you’ve got your line!