Final answer:
In the linear equation 1 plus 4 x plus 6 minus x equals y, the slope (m) is 3 and the y-intercept (b) is 7, after simplifying the equation to 3x + 7 = y.
Step-by-step explanation:
In the linear equation 1 plus 4 x plus 6 minus x equals y, the terms m and b represent the slope and y-intercept of the equation, respectively. To identify these terms, we must first simplify the equation. We combine like terms to get 3x + 7 = y. Here, 3 is the coefficient of x, which is the slope (m) of the line, and 7 is the constant term, which is the y-intercept (b).
The slope (m) is defined as the rise over the run between any two distinct points on the line. In this case, with each increase of 1 in x (the run), y increases by 3 (the rise), hence the slope is 3. The y-intercept (b) is the value where the line crosses the y-axis, which occurs when x equals 0. In this equation, when x = 0, y = 7, which means the line crosses the y-axis at the point (0, 7).