Question

identify the slope and y-intercept of each line. then write an equation in slope-intercept form.
(there are two graphs of lines on coordinate planes, each with spaces to fill in slope (m), y-intercept (b), and the equation. for the first graph: m = ____ b = __ equation: ________ for the second graph: m = __ b = __ equation: __________)

Explanation:

Left Graph:

Step1: Find y-intercept ($b$)

The line crosses the y-axis at $(0, 2)$, so $b=2$.

Step2: Calculate slope ($m$)

Use two points $(0,2)$ and $(1,0)$:
$m=\frac{0-2}{1-0}=-2$

Step3: Write slope-intercept equation

Slope-intercept form is $y=mx+b$, substitute $m=-2$ and $b=2$:
$y=-2x+2$

Right Graph:

Step1: Find y-intercept ($b$)

The line crosses the y-axis at $(0, -4)$, so $b=-4$.

Step2: Calculate slope ($m$)

Use two points $(0,-4)$ and $(2,2)$:
$m=\frac{2-(-4)}{2-0}=\frac{6}{2}=3$

Step3: Write slope-intercept equation

Slope-intercept form is $y=mx+b$, substitute $m=3$ and $b=-4$:
$y=3x-4$

Answer:

Left Graph:

$m = -2$
$b = 2$
Equation: $y=-2x+2$

Right Graph:

$m = 3$
$b = -4$
Equation: $y=3x-4$