To write the equation of a line in slope-intercept form $y = mx + b$, we need the slope $m$ and the y-intercept $b$.

Given:

• Point $(-1, -8)$
• Slope $m = 5$

We can use the point-slope form of a line: $y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is a point on the line. Substituting the values:

$y - (-8) = 5(x - (-1))$

Simplify: $y + 8 = 5(x + 1)$

Expanding this: $y + 8 = 5x + 5$

Subtract 8 from both sides to isolate $y$: $y = 5x - 3$

Final Answer

The equation of the line in slope-intercept form is: $y = 5x - 3$

Would you like further details or have any questions?

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Here are five related questions for practice:

1. How would you find the equation of a line passing through $(2, 3)$ with a slope of $-4$?
2. If a line has a slope of $0$, what is its equation if it passes through $(1, -5)$?
3. How can you determine if two lines are parallel given their equations?
4. How would you convert the equation $3x + 4y = 12$ to slope-intercept form?
5. What is the equation of a line perpendicular to $y = 2x + 1$ that passes through $(3, 4)$?

Tip: When finding the equation of a line with a known slope and point, the point-slope form $y - y_1 = m(x - x_1)$ is often the most direct method.