Final answer:
The slope of the line passing through the points (2, 3) and (-1, -6) is -3. The point-slope form of the equation is y - 3 = -3(x - 2), and the slope-intercept form is y = -3x + 9.
Step-by-step explanation:
To find the slope of a line passing through two points (2, 3) and (-1, -6), we use the slope formula, which is (y₂ - y₁) / (x₂ - x₁). Thus, the slope is (-6 - 3) / (-1 - 2) which equals 9 / -3, yielding -3 as the slope.
To write the equation of the line in point-slope form, we can use one of the points and the slope. The formula is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is one of the points. Hence, using the point (2, 3) the equation is: y - 3 = -3(x - 2).
Finally, to rewrite the equation in slope-intercept form, we solve for y to get y = mx + b. Expanding the point-slope form, y - 3 = -3x + 6, and adding 3 to both sides, we get y = -3x + 9 as the slope-intercept form.