Write y = (1/4)(x + 1) - 2 in slope-intercept form and state the slope and y-intercept.

Step-by-step solution

1. 1

   Recognise the starting form. $y=\tfrac14(x+1)-2$ is a shifted version of point-slope form: the coefficient outside the bracket is already the slope, and the goal is to expose the $y$-intercept.

2. 2

   Distribute the $\tfrac14$ over the bracket. Both terms inside must be multiplied:

   $y=\frac{1}{4}x+\frac{1}{4}(1)-2=\frac{1}{4}x+\frac{1}{4}-2$

3. 3

   Combine the constants over a common denominator. Write $2$ as $\tfrac84$:

   $\frac{1}{4}-2=\frac{1}{4}-\frac{8}{4}=-\frac{7}{4}$

4. 4

   State the slope-intercept form.

   $y=\frac{1}{4}x-\frac{7}{4}$

   so the slope is $m=\tfrac14$ and the $y$-intercept is $c=-\tfrac74=-1.75$.

5. 5

   Check with two points. At $x=0$ the original gives $\tfrac14(1)-2=-1.75$, matching the intercept $\checkmark$. At $x=3$ the original gives $\tfrac14(4)-2=-1$, and the new form gives $\tfrac34-\tfrac74=-1$ $\checkmark$. The slope check: $y$ rose by $0.75$ while $x$ rose by $3$, and $\tfrac{0.75}{3}=\tfrac14$ $\checkmark$.