Question

what is the equation of the top line graphed below?

a. $y = b(mx)$

b. $y = mx + b$

c. $y = \frac{1}{b}(mx)$

Explanation:

Step1: Recall Slope-Intercept Form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The blue line is $y=mx$, which passes through the origin $(0,0)$ (so its y - intercept $b = 0$). The red line (top line) is parallel to the blue line, so it has the same slope $m$. But it has a y - intercept of $b$ (since it crosses the y - axis at a value of $b$ above the origin).

Step2: Analyze the Options

• Option A: $y = b(mx)$ is not the slope - intercept form. It represents a different type of function (a product of a constant and a linear term), not a linear function with a y - intercept.
• Option B: $y=mx + b$ is the slope - intercept form. Since the red line has the same slope $m$ as the blue line $y = mx$ and a y - intercept of $b$, this equation matches the graph of the red line.
• Option C: $y=\frac{1}{b}(mx)$ is also not the slope - intercept form. It is a scaled version of the linear term $mx$, not a linear function with a y - intercept.

Answer:

B. $y = mx + b$