Question

y-intercept=-2
(-2, 6)
y-intercept
what is the y-intercept of the blue line?

Explanation:

Step1: Recall line equation form

The slope-intercept form of a line is $y = mx + b$, where $b$ is the y-intercept, and $m$ is the slope.

Step2: Calculate the slope

Use the two points $(-2, 6)$ and $(2, 4)$. The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$.
$m = \frac{4 - 6}{2 - (-2)} = \frac{-2}{4} = -\frac{1}{2}$

Step3: Substitute point to find $b$

Plug $x = -2$, $y = 6$, and $m = -\frac{1}{2}$ into $y = mx + b$.
$6 = -\frac{1}{2}(-2) + b$
$6 = 1 + b$

Step4: Solve for $b$

Subtract 1 from both sides:
$b = 6 - 1 = 5$

Answer:

The y-intercept of the blue line is $\boldsymbol{5}$ (or the point $(0, 5)$)