Final answer:
The equation (y - 1) = 4(x - 2) is converted to slope-intercept form by distributing the 4, adding 1 to both sides, and combining like terms to achieve y = 4x - 7, where the slope is 4 and the y-intercept is -7.
Step-by-step explanation:
To convert the equation (y - 1) = 4(x - 2) from point-slope form to slope-intercept form, we must first distribute the slope on the right-hand side of the equation across the (x - 2). This gives us:
y - 1 = 4x - 8
Next, to isolate the y-variable, we add 1 to both sides of the equation:
y = 4x - 8 + 1
Finally, we combine like terms to find the slope-intercept form of the equation:
y = 4x - 7
The slope-intercept form y = mx + b uses m to represent the slope and b to represent the y-intercept. In this case, m = 4, which is the slope, and b = -7, which is the y-intercept of the line.