Final answer:
To find the equation of a line with a given slope and point, we can use the point-slope form of a linear equation. By plugging in the values, we can solve for the equation in the slope-intercept form, y = mx + b. The slope (m) and y-intercept (b) can be identified from the equation.
Step-by-step explanation:
To find the equation of the line with slope -3 and containing the point (-9, -4), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). Plugging in the values, we get y - (-4) = -3(x - (-9)). Simplifying, we have y + 4 = -3x - 27. Rearranging the equation to the slope-intercept form, y = -3x - 31. Therefore, the equation of the line is y = -3x - 31, where m = -3 and b = -31.
For the second question, to find the equation of the line passing through the points (3, 2) and (6, 8), we can first find the slope using the formula m = (y2 - y1) / (x2 - x1). Plugging in the values, we get m = (8 - 2) / (6 - 3) = 6 / 3 = 2. Now, we can use the point-slope form with one of the given points (3, 2) to get y - 2 = 2(x - 3). Simplifying, we have y - 2 = 2x - 6. Rearranging the equation to the slope-intercept form, y = 2x - 4. Therefore, the equation of the line is y = 2x - 4, where m = 2 and b = -4.