Final answer:
The slope and y-intercept of each given linear equation are identified by re-arranging them into the y = mx + b format, where m is the slope and b is the y-intercept. These values characterize the steepness and the point where the line crosses the y-axis, respectively.
Step-by-step explanation:
To write the slope and y-intercept for each equation, we want them in the y = mx + b format, where m is the slope and b is the y-intercept.
- A) y = -5x + 46 Slope: -5, Y-intercept: 46
- B) 3x - 2y = 1 (To get this in y = mx + b format, we solve for y: -2y = -3x + 1, then divide each term by -2, resulting in y = 3/2x - 1/2) Slope: 3/2, Y-intercept: -1/2
- C) y = -2x - 4 Slope: -2, Y-intercept: -4
- D) y = 8x + 1 Slope: 8, Y-intercept: 1
- E) y = 5x - 3 Slope: 5, Y-intercept: -3
- F) y = -3x - 9 Slope: -3, Y-intercept: -9
- G) y = 7x + 2 Slope: 7, Y-intercept: 2
- H) y = -6x + 6 Slope: -6, Y-intercept: 6
All of these equations are examples of linear equations which graph as straight lines with consistent slopes throughout.