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We are tasked with finding which equation will pass through the points \((0, -3)\) and \((5, 7)\). Let's determine the slope and equation of the line that passes through these points.

### Step 1: Calculate the slope
The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

For the points \((0, -3)\) and \((5, 7)\):

\[
m = \frac{7 - (-3)}{5 - 0} = \frac{7 + 3}{5} = \frac{10}{5} = 2
\]

### Step 2: Find the equation using the slope-intercept form
Now that we have the slope \( m = 2 \), we can use the point-slope form of the line equation:

\[
y - y_1 = m(x - x_1)
\]

Using the point \((0, -3)\):

\[
y - (-3) = 2(x - 0)
\]
\[
y + 3 = 2x
\]
\[
y = 2x - 3
\]

### Conclusion:
The equation of the line that passes through the points \((0, -3)\) and \((5, 7)\) is \( y = 2x - 3 \).

From the given options, the correct choice is **B. \( y = 2x - 3 \)**.

Would you like more details on this or have any other questions?

Here are 5 related questions to expand on this concept:
1. How do you find the equation of a line given a point and a slope?
2. What is the significance of the slope in a linear equation?
3. How can you verify if a point lies on a given line?
4. How do different forms of the equation of a line (e.g., slope-intercept, point-slope) relate to each other?
5. How do you calculate the slope when both points have the same x-coordinate?

**Tip:** To check if a point lies on a line, substitute the point’s coordinates into the equation and see if the equation holds true.

The graph of which equation will pass through points (0, -3) and (5, 7)?

Find the equation of the line passing through the points (0, -3) and (5, 7) using the slope-intercept form. This problem explores key concepts in linear equations and slope calculation, suitable for students in Grades 8-10.

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