Question

a box is \\(\frac{1}{4}\\) inch taller than it is wide. let h = height. let w = width. complete the table, and graph \\(h = w + \frac{1}{4}\\). the table has \\(h = w + \frac{1}{4}\\) at the top, with columns w and h, and rows with w values 1, 2, 3, and empty h cells. (type integers, fractions, or mixed numbers.)

Explanation:

Step1: Calculate h when w=1

Substitute $w=1$ into $h=w+\frac{1}{4}$
$h=1+\frac{1}{4}=\frac{5}{4}$ or $1\frac{1}{4}$

Step2: Calculate h when w=2

Substitute $w=2$ into $h=w+\frac{1}{4}$
$h=2+\frac{1}{4}=\frac{9}{4}$ or $2\frac{1}{4}$

Step3: Calculate h when w=3

Substitute $w=3$ into $h=w+\frac{1}{4}$
$h=3+\frac{1}{4}=\frac{13}{4}$ or $3\frac{1}{4}$

Answer:

$w$	$h$
2	$\frac{9}{4}$ (or $2\frac{1}{4}$)
3	$\frac{13}{4}$ (or $3\frac{1}{4}$)

For the graph of $h=w+\frac{1}{4}$: This is a linear graph with a slope of 1 and a y-intercept (h-intercept here) of $\frac{1}{4}$. Plot the points $(1, \frac{5}{4})$, $(2, \frac{9}{4})$, $(3, \frac{13}{4})$ and draw a straight line through them.