Final answer:
To write a linear equation with specific criteria, we can use different forms of linear equations based on the given conditions. For part A, a standard form equation with a positive slope and a negative y-intercept can be written as 2x - 3y = -6. For part B, a slope-intercept form equation with a negative slope and a y-intercept of 0 is y = -0.5x. For part C, a point-slope form equation with a negative slope and a positive y-intercept can be written as y - 4 = -2(x - 3). And finally, for part D, a zero-slope line can be represented by simply setting y equal to a constant value, such as y = 5.
Step-by-step explanation:
A. To write a standard form equation with a positive slope and a negative y-intercept, we can use the form Ax + By = C, where A, B, and C are constants. Let’s say we choose A = 2, B = -3, and C = -6. The equation would be 2x - 3y = -6.
B. To write a slope-intercept form equation with a negative slope and a y-intercept of 0, we can use the form y = mx + b, where m is the slope and b is the y-intercept. Let’s say we choose m = -0.5. The equation would be y = -0.5x.
C. To write a point-slope form equation with a negative slope and a positive y-intercept, we can use the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Let’s say we choose (x1, y1) = (3, 4) and m = -2. The equation would be y - 4 = -2(x - 3).
D. A zero-slope line is a horizontal line. We can write an equation for a horizontal line at some positive value by setting y equal to that value. For example, the equation y = 5 represents a horizontal line at y = 5.