To determine the equation of line B, we can use the two points provided: $(-3, 5)$ and $(1, 0)$.

Step 1: Calculate the slope (m)

The formula for the slope between two points is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the coordinates $(-3, 5)$ and $(1, 0)$:

$m = \frac{0 - 5}{1 - (-3)} = \frac{-5}{1 + 3} = \frac{-5}{4}$

So, the slope $m = -\frac{5}{4}$.

Step 2: Use the point-slope form

Now that we have the slope, we can use the point-slope form of a line equation:

$y - y_1 = m(x - x_1)$

We'll use the point $(1, 0)$:

$y - 0 = -\frac{5}{4}(x - 1)$

Simplify:

$y = -\frac{5}{4}(x - 1)$

Distribute the slope:

$y = -\frac{5}{4}x + \frac{5}{4}$

Final Equation

Thus, the equation of line B is:

$y = -\frac{5}{4}x + \frac{5}{4}$

Let me know if you need any more details or if this equation matches one of the provided answer options.

Related Questions:

1. How do you convert a slope-intercept equation into point-slope form?
2. What is the general form of a linear equation, and how do you convert between forms?
3. How does the slope of a line relate to its steepness and direction?
4. What are the different methods to find the equation of a line from a graph?
5. How can we find the x- and y-intercepts from a given line equation?

Tip:

When identifying the equation of a line from a graph, always double-check the slope by using at least two distinct points to avoid small calculation errors.