Final answer:
The inequalities given are already in slope-intercept form, representing lines with slopes of 2 or -2 and y-intercepts at 3 or -3, designating regions above or below these lines.
Step-by-step explanation:
The student's question involves converting a system of inequalities to slope-intercept form. The slope-intercept form of an equation is y = mx + b, where m represents the slope and b represents the y-intercept. Here, we have four inequalities:
- (a) y < 2x + 3
- (b) y > 2x - 3
- (c) y < -2x + 3
- (d) y > -2x - 3
Each of these inequalities already is in the slope-intercept form, where the inequality symbolizes the area above (>) or below (<) the line on a graph that the equation would create. For instance, inequality (a) has a slope (m) of 2, meaning for every increase of 1 on the horizontal axis, there is a rise of 2 on the vertical axis, and it has a y-intercept (b) of 3, which is where the line would cross the y-axis. Inequality (b) also has a slope of 2 but a y-intercept of -3, indicating it would cross the y-axis lower than inequality (a). Inequities (c) and (d) have a negative slope (-2) which means the line would slope downward to the right, with their respective y-intercepts at 3 and -3.