OPTION #1 is correct, the equation of the line is y = (3/2)x.
OPTION #5 is correct, she averages 3 new students every 2 weeks.
OPTION #6 is correct, the slope is 3/2.
Explanation:
To put it simply, slope can be described as rise over run. Rise being (vertical) y values and run being (horizontal) x values.
First pick two points on the graph like (0,0) and (4,6). From the origin to the second point, it is +6 rise (upwards) and +4 run (to the right). This is expressed as 6/4 and simplifies to 3/2. The slope of the line = (3/2).
—OPTION #6 is correct, the slope is 3/2.
—Option #4 is now confirmed incorrect as the slope is not written correctly here.
—Option #2 does not work because for every 3 x-values, the y-values increase by 4. She gets 4 students each 3 weeks, not 2 students, so it is not correct.
—Option #5, on the other hand, IS correct. You can trace this on the graph by looking at the point (2,3) and (4,6). The y-axis is for the number of students and the x-axis is for the number of weeks; points written as (x, y). From the first point at 2 weeks to the second at 4 weeks, the number of students increased by 3.
—Option #3 is incorrect; for slope intercept form, y = mx + b, m is the slope and b is the y-intercept. On this graph the y-int = 0. The equation y = 3x + 2 does not create the graph above. The slope is not 3, and the graph starts at the origin, meaning it is not translated up +2 units like this equation.