Question

this table shows some values of a linear function, $h(x)$. complete the table.
write your answers as whole numbers, decimals, or simplified fractions or mixed numbers.
$x$ $h(x)$
$-7$ $\frac{25}{3}$
$-6$ $7$
$-5$
$-4$
$-3$

Explanation:

Step1: Find slope m

First, convert 7 to $\frac{21}{3}$. Use points $(-7, \frac{25}{3})$ and $(-6, \frac{21}{3})$.
$m = \frac{\frac{21}{3} - \frac{25}{3}}{-6 - (-7)} = \frac{-\frac{4}{3}}{1} = -\frac{4}{3}$

Step2: Define linear function

Use point-slope form with $(-6, 7)$:
$h(x) - 7 = -\frac{4}{3}(x - (-6))$
Simplify: $h(x) = -\frac{4}{3}x - 8 + 7 = -\frac{4}{3}x - 1$

Step3: Calculate h(-5)

Substitute $x=-5$ into the function:
$h(-5) = -\frac{4}{3}(-5) - 1 = \frac{20}{3} - \frac{3}{3} = \frac{17}{3}$

Step4: Calculate h(-4)

Substitute $x=-4$ into the function:
$h(-4) = -\frac{4}{3}(-4) - 1 = \frac{16}{3} - \frac{3}{3} = \frac{13}{3}$

Step5: Calculate h(-3)

Substitute $x=-3$ into the function:
$h(-3) = -\frac{4}{3}(-3) - 1 = 4 - 1 = 3$

Answer:

$x$	$h(x)$
-6	$7$
-5	$\frac{17}{3}$
-4	$\frac{13}{3}$
-3	$3$