Final answer:
The equation of the line with a y-intercept of 4 and a slope of -1 is y = -x + 4. For a line through point (3,4) with a slope of -2, the equation is y = -2x + 10. For a line through points (1, -1) and (9,3), the equation is y = 0.5x - 1.5.
Step-by-step explanation:
To find the equation of a line in slope-intercept form, which is y = mx + b, we need to know the slope (m) and y-intercept (b). For part (a), given a y-intercept of 4 and a slope of -1, the equation of the line is y = -x + 4.
For part (b), given the point (3,4) and a slope of -2, we use the point-slope form y - y1 = m(x - x1) and plug in the values to get y - 4 = -2(x - 3), which simplifies to y = -2x + 10.
For part (c), we first calculate the slope using the points (1, -1) and (9,3) which gives us a slope of (3 - (-1))/(9 - 1) = 4/8 = 0.5. Using the point-slope form with one of the points, say (1, -1), we get y + 1 = 0.5(x - 1), which simplifies to y = 0.5x - 1.5.