To determine which equations and/or functions represent the graphed line with a slope of 3 and a y-intercept of 2, we can compare the given options with the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Given:
Slope = 3
Y-intercept = 2
Now, we can check each option:
A. f(x) = 1/5x - 4
This equation has a slope of 1/5, not matching the given slope of 3.
B. f(x) = 1/2x + 2
This equation has a slope of 1/2, not matching the given slope of 3.
C. f(x) = 1/2x + 1
This equation has a slope of 1/2, not matching the given slope of 3.
D. y - 3 = 1/2(x - 2)
By rearranging this equation into slope-intercept form (y = mx + b), we get:
y = 1/2x + 2
This equation matches the given slope of 3 but not the y-intercept of 2.
E. y - 1 = 1/2(x + 2)
By rearranging this equation into slope-intercept form (y = mx + b), we get:
y = 1/2x + 1
This equation doesn't match the given slope of 3 or the y-intercept of 2.
Among the options provided, none of the equations perfectly match the given slope of 3 and y-intercept of 2.
