Question

what is the equation of the line shown in this graph?
drag and drop the expressions to write the equation of the line in slope - intercept form.
the graph has points (1,2) and (4, - 4) and a coordinate grid with axes labeled x and y.

Explanation:

Step1: Identify slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$
Use points $(1,2)$ and $(4,-4)$:
$m = \frac{-4 - 2}{4 - 1} = \frac{-6}{3} = -2$

Step2: Find y-intercept $b$

Use slope-intercept form $y = mx + b$, substitute $m=-2$ and point $(1,2)$:
$2 = -2(1) + b$
$2 = -2 + b$
$b = 2 + 2 = 4$

Step3: Write final equation

Combine $m=-2$ and $b=4$ into $y=mx+b$:
$y = -2x + 4$

Answer:

$y = -2x + 4$