Question

there is a grid graph with x - axis from 0 to 20 and y - axis from 0 to 11. a red line passes through some points. there is also a table with columns x and y, where x values are 10 (y = 5), 16 (y is blank), 18 (y is blank), 19 (y = 14). and there is an equation y = (blank) to be filled.

Explanation:

Step1: Find slope using two points

Use points $(10,5)$ and $(19,14)$. Slope $m=\frac{y_2-y_1}{x_2-x_1}=\frac{14-5}{19-10}=\frac{9}{9}=1$

Step2: Find y-intercept $b$

Substitute $m=1$, $x=10$, $y=5$ into $y=mx+b$:
$5=1(10)+b \implies b=5-10=-5$

Step3: Write linear equation

$y = x - 5$

Step4: Calculate $y$ for $x=16$

Substitute $x=16$ into $y=x-5$:
$y=16-5=11$

Step5: Calculate $y$ for $x=18$

Substitute $x=18$ into $y=x-5$:
$y=18-5=13$

Answer:

For $x=16$, $y=11$
For $x=18$, $y=13$
Linear equation: $y = x - 5$