To solve this problem, we need to write the equation of a line in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The line passes through the points $(-5, -2)$ and $(5, 4)$.

Step 1: Calculate the slope ($m$):

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the given points $(-5, -2)$ and $(5, 4)$: $m = \frac{4 - (-2)}{5 - (-5)} = \frac{4 + 2}{5 + 5} = \frac{6}{10} = \frac{3}{5}$ So, the slope is $m = \frac{3}{5}$.

Step 2: Use point-slope form to find the equation:

The point-slope form is: $y - y_1 = m(x - x_1)$ We can use one of the points, for example $(-5, -2)$, and substitute $m = \frac{3}{5}$: $y - (-2) = \frac{3}{5}(x - (-5))$ Simplify: $y + 2 = \frac{3}{5}(x + 5)$

Step 3: Solve for $y$ to get the slope-intercept form:

Distribute $\frac{3}{5}$: $y + 2 = \frac{3}{5}x + \frac{15}{5}$ $y + 2 = \frac{3}{5}x + 3$ Subtract 2 from both sides: $y = \frac{3}{5}x + 1$

Final Answer:

The equation of the line is: $y = \frac{3}{5}x + 1$

Would you like me to explain any part of the process in more detail?

Here are 5 related questions for further practice:

1. How do you find the slope of a line given two points?
2. How do you convert from point-slope form to slope-intercept form?
3. What is the y-intercept of the line $y = \frac{3}{5}x + 1$?
4. How do you graph the line $y = \frac{3}{5}x + 1$?
5. What is the equation of the line parallel to $y = \frac{3}{5}x + 1$ that passes through the origin?

Tip: Always double-check your slope calculations when working with points to avoid errors in your equation.