Final answer:
All options presented, A) y=2x+1, B) y=-2x+3, C) y=3x-2, and D) y=-3x+2, represent linear equations in the simplified slope-intercept form. To determine the correct answer among these, further context or specifications from the student would be necessary.
Step-by-step explanation:
The student's question asks for the fully simplified equation of a line in slope-intercept form, which is expressed as y = mx + b, where m is the slope and b is the y-intercept. To choose between the options provided, we must identify which choice correctly represents a line in slope-intercept form.
Let's evaluate the options by recalling the information given in the question's reference materials. According to 'Slope and y-intercept of a Linear Equation', the form y = a + bx is used and is equivalent to the slope-intercept form y = mx + b. In both cases, the coefficient of x is the slope, and the constant number is the y-intercept.
With this in mind:
- Option A) y = 2x + 1 is in slope-intercept form with a slope of 2 and a y-intercept of 1.
- Option B) y = -2x + 3 is also in slope-intercept form with a slope of -2 and a y-intercept of 3.
- Option C) y = 3x - 2 is in slope-intercept form with a slope of 3 and a y-intercept of -2.
- Option D) y = -3x + 2 is in slope-intercept form with a slope of -3 and a y-intercept of 2.
All options, A), B), C), and D), represent linear equations in the slope-intercept form. For an equation to be considered fully simplified, it must demonstrate the variables and numbers in their most reduced form, which all options are doing. Therefore, without additional context, any of these could be the correct answer. However, if the student provided more details, such as the slope or y-intercept, a specific choice could be made. Since we are tasked to identify the fully simplified equation of the line, and all options are in their simplest form, we may need to refer back to the student's original question for more information or clarification.