21. write the linear equation whose graph is shown in the form y = mx + b.
21. write the linear equation whose graph is shown in the form y = mx + b.
Answer
Explanation:
Step1: Find the slope $m$
The line passes through points $(2,2)$ and $(3,4)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m=\frac{4 - 2}{3 - 2}=2$.
Step2: Find the y - intercept $b$
Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(2,2)$ and $m = 2$. We get $y-2=2(x - 2)$. Expand it: $y-2=2x-4$. Then $y=2x-2$, so $b=-2$.
Answer:
$y = 2x-2$