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 first point coordinates

The lower point has $x=0.6$, $y=6$, so coordinates $(0.6, 6)$.

Step2: Identify second point coordinates

The upper point has $x=1.10$, $y=10$, so coordinates $(1.10, 10)$.

Step3: Calculate vertical distance

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

Step4: Calculate horizontal distance

Subtract x-values: $1.10 - 0.6 = 0.5$

Step5: Compute slope

Divide vertical by horizontal distance: $\frac{4}{0.5} = 8$

Step6: Find vertical intercept

Use $y=mx+b$, plug $(0.6,6)$ and $m=8$:
$6 = 8(0.6) + b$
$6 = 4.8 + b$
$b = 6 - 4.8 = 1.2$

Step7: Write line equation

Substitute $m=8$, $b=1.2$ into $y=mx+b$

Answer:

Labeled points: $(0.6, 6)$ and $(1.10, 10)$
Slope: $8$
Vertical intercept: $1.2$
Line equation: $y = 8x + 1.2$