To find the equation of the line that passes through two points, we follow these steps:

1. Find the slope using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.

2. Use the point-slope form of a line equation: $y - y_1 = m(x - x_1)$ and convert it to the slope-intercept form $y = mx + b$.

Step 1: Calculate the slope $m$

We have the points $(-2, 2)$ and $(2, -8)$.

$m = \frac{-8 - 2}{2 - (-2)} = \frac{-10}{4} = -\frac{5}{2}$

Step 2: Use point-slope form

We can choose one of the points, say $(-2, 2)$, to substitute into the point-slope form.

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

Simplify the equation:

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

Final Answer:

The equation of the line in slope-intercept form is: $y = -\frac{5}{2}x - 3$

Would you like further details or have any questions?

Related Questions:

1. How do you derive the equation of a line from its slope and a point on the line?
2. What is the significance of the slope in the slope-intercept form?
3. How do you convert point-slope form to slope-intercept form?
4. What are the steps to graph a line given its equation in slope-intercept form?
5. How can you check if a point lies on a given line?

Tip:

When calculating the slope, always be careful with the signs of the coordinates to avoid mistakes in the equation.