Question

complete the table and write the equation for the relationship shown in the graph.

Explanation:

Step1: Identify intercept points

From the graph, the line passes through $(5,0)$ and $(0,-5)$ (implied, since slope is 1: when $x$ increases by 1, $y$ increases by 1; so when $x=0$, $y=0-5=-5$).

Step2: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{2-0}{7-5}=\frac{2}{2}=1$

Step3: Write slope-intercept equation

Slope-intercept form: $y=mx+b$, where $b=-5$
$y=1\cdot x - 5$

Step4: Build the table (sample values)

Choose $x$ values, compute $y$:

• $x=5$: $y=5-5=0$
• $x=7$: $y=7-5=2$
• $x=10$: $y=10-5=5$
• $x=15$: $y=15-5=10$
• $x=19$: $y=19-5=14$

Answer:

Completed Table (sample):

$x$	$y$
7	2
10	5
15	10
19	14

Equation:

$y = x - 5$