Final Answer:
The equation y = 4x - 2 in slope-intercept form is y = mx + b, where m represents the slope of the line and b is the y-intercept. In this equation, the slope is 4, and the y-intercept is -2.
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where 'm' represents the slope of the line, and 'b' represents the y-intercept. In the given equation y = 4x - 2, '4x' is the term involving the slope (m), and '-2' is the y-intercept (b).
To express the equation in slope-intercept form, we isolate 'y' on one side of the equation. Starting with y = 4x - 2, we observe that the equation is already in the required form: y = mx + b. Here, the coefficient of 'x' (4) represents the slope of the line. Therefore, the slope of this line is 4, indicating that for every increase of one unit in the x-direction, the y-value increases by 4 units.
Moreover, the constant term '-2' represents the y-intercept, which is the point where the line intersects the y-axis. In this case, the y-intercept is at -2 on the y-axis. Hence, this line crosses the y-axis at the point (0, -2). In summary, the equation y = 4x - 2 represents a line with a slope of 4 and a y-intercept of -2, demonstrating its behavior and position on the coordinate plane.