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{\text{vertical distance}}{\text{horizontal distance}}\\)

Explanation:

Step1: Identify coordinates of first point

The lower point has an x-value of 0, so its coordinates are $(0, 6)$.

Step2: Identify coordinates of second point

The upper point has an x-value of 1, so its coordinates are $(1, 10)$.

Step3: Calculate vertical distance

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

Step4: Calculate horizontal distance

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

Step5: Compute the slope

Use slope formula: $\text{slope} = \frac{\text{vertical distance}}{\text{horizontal distance}} = \frac{4}{1} = 4$

Step6: Find vertical intercept

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

Step7: Write line equation

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

Answer:

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