The image appears to be a mathematical problem involving finding the equation of a line passing through two points, labeled $A(-1, 3)$ and $B(4, 5)$.

To find the equation of the line through these two points, we can use the point-slope form of the line equation, which is given by:

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

where:

• $m$ is the slope of the line, calculated as $m = \frac{y_2 - y_1}{x_2 - x_1}$
• $(x_1, y_1)$ is a point on the line.

Step 1: Calculate the slope The coordinates of the points are $A(-1, 3)$ and $B(4, 5)$.

The slope $m$ is:

$m = \frac{5 - 3}{4 - (-1)} = \frac{2}{5}$

Step 2: Use the point-slope form We can use either point for $(x_1, y_1)$. Let's use point $A(-1, 3)$.

$y - 3 = \frac{2}{5}(x - (-1))$

Simplify the equation:

$y - 3 = \frac{2}{5}(x + 1)$

Distribute the $\frac{2}{5}$:

$y - 3 = \frac{2}{5}x + \frac{2}{5}$

Step 3: Solve for $y$

$y = \frac{2}{5}x + \frac{2}{5} + 3$

Simplify further:

$y = \frac{2}{5}x + \frac{17}{5}$

Thus, the equation of the line is:

$y = \frac{2}{5}x + \frac{17}{5}$

Let me know if you'd like more details or further steps explained!

Related Questions:

1. How do you find the slope between two given points?
2. How do you use the point-slope form to write the equation of a line?
3. What is the difference between point-slope form and slope-intercept form?
4. How do you graph the equation of a line once you have the equation?
5. What happens to the slope if the points are vertical or horizontal?

Tip: Always check that the slope calculation makes sense — a horizontal line has a slope of 0, and a vertical line has an undefined slope!