which equation represents the graphed function?\n$y = 4x - 2$\n$y=-4x - 2$\n$y=\frac{1}{4}x - 2$\n$y…
which equation represents the graphed function?\n$y = 4x - 2$\n$y=-4x - 2$\n$y=\frac{1}{4}x - 2$\n$y =-\frac{1}{4}x - 2$
Answer
Explanation:
Step1: Recall slope - intercept form
The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
Step2: Find the y - intercept
The line crosses the y - axis at the point $(0,-2)$, so $b=-2$.
Step3: Calculate the slope
The slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(0,-2)$ and $(4,-1)$, we have $m=\frac{-1-(-2)}{4 - 0}=\frac{-1 + 2}{4}=\frac{1}{4}$.
Step4: Determine the equation
Substituting $m = \frac{1}{4}$ and $b=-2$ into $y=mx + b$, we get $y=\frac{1}{4}x-2$.
Answer:
$y=\frac{1}{4}x - 2$