Question

youre trying to write an equation that represents this line by finding the slope and vertical intercept. remember, the slope is the change in vertical distance for a given change in horizontal distance. we can use any two points on the line to find the slope. label the coordinates of the two points on the graph below. slope = \frac{vertical distance}{horizontal distance}

Explanation:

Step1: Identify coordinates of points

The lower point is $(0, 6)$; the upper point is $(1, 10)$.

Step2: Calculate vertical distance

Subtract y-values: $10 - 6 = 4$

Step3: Calculate horizontal distance

Subtract x-values: $1 - 0 = 1$

Step4: Compute the slope

Divide vertical by horizontal distance: $\frac{4}{1} = 4$

Step5: Identify vertical intercept

The vertical intercept is the y-value when $x=0$, which is 6.

Step6: Write line equation

Use $y = mx + b$ where $m=4$, $b=6$: $y = 4x + 6$

Answer:

Labeled points: $(0, 6)$ and $(1, 10)$
Slope: $4$
Vertical intercept: $6$
Line equation: $y = 4x + 6$