Question

which equation best represents the relationship between x and y in the graph?
a. y = 6x + 1
b. y = 3.5x + 1
c. y = 2.5x + 1
d. y = 3x + 1

Explanation:

Step1: Recall slope - intercept form

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

Step2: Find the y - intercept

The line crosses the y - axis at $y = 1$, so $b = 1$ for all the given options.

Step3: Estimate the slope

Pick two points on the line, say $(0,1)$ and $(2,8)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{8 - 1}{2-0}=\frac{7}{2}=3.5$

Answer:

B. $y = 3.5x+1$