Final answer:
The equation y - 5 = 4(x - 1) is manipulated into y = mx + b form to get y = 4x + 1, where the slope m is 4 and the y-intercept b is 1, representing how to express equations graphically on a plot.
Step-by-step explanation:
To write the equation y - 5 = 4(x - 1) in the y = mx + b form, we have to isolate y and simplify the right side of the equation. Here's how we do it step by step:
- Start by expanding the right side of the equation: y - 5 = 4x - 4.
- Add 5 to both sides of the equation to get y alone on one side: y = 4x - 4 + 5.
- Combine like terms on the right side to simplify the equation: y = 4x + 1.
Now, we have the equation in the desired linear equation form, where m is the slope, and the b is the y-intercept. In this case, m = 4, which is the slope, and b = 1, which represents the y-intercept. This equation shows how to express equations graphically by plotting them on a graph with the given slope and y-intercept. By using different values for x, we could create points that fall on the line represented by the equation and draw the line through these points.