5. write the equation of the line represented by the following graph (2 points):
5. write the equation of the line represented by the following graph (2 points):
Answer
Explanation:
Step1: Find the slope
The line passes through points $(0, - 2)$ and $(2,0)$. The slope $m$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m=\frac{0-\left(-2\right)}{2 - 0}=\frac{2}{2}=1$.
Step2: Find the y - intercept
The y - intercept $b$ is the y - value when $x = 0$. From the graph, when $x = 0$, $y=-2$, so $b=-2$.
Step3: Write the equation of the line
The slope - intercept form of a line is $y=mx + b$. Substituting $m = 1$ and $b=-2$ into the equation, we get $y=x - 2$.
Answer:
$y=x - 2$