Question

write the equation for the relationship shown in the graph.

Explanation:

Step1: Identify slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$.

Step2: Pick two points from graph

Choose $(5,4)$ and $(15,14)$.

Step3: Calculate the slope

$m=\frac{14-4}{15-5}=\frac{10}{10}=1$

Step4: Use point-slope form

Point-slope form: $y-y_1=m(x-x_1)$. Use $(5,4)$:
$y-4=1(x-5)$

Step5: Simplify to slope-intercept form

$y-4=x-5$
$y=x-5+4$
$y=x-1$

Answer:

$y = x - 1$