Answer:
No answer option has a slope of (2/5).
Explanation:
The standard form of a line in slope intercept form is y = mx + b, where m is the slope and b is the y-intercept (the value of y when x is zero).
We are give the slope as (2/5) so we can write:
y = (2/5)x + b
To find b, we can enter the one known point that is on the line, (-2,4):
y = (2/5)x + b
y = (2/5)x + b for (-2,4)
(4) = (2/5)(-2) + b for (-2,4)
4 = -(4/5) + b
b = 4 + (4/5)
b = (20/5) + (4/5)
b = (24/5)
The full equation is y = (4/5)x + (24/5)
This can be written as:
y = (4/5)x + (24/5)
5y = 4x + 24
None of the answer options has a slope of (2/5)
We can rewrite the answer options to put them into slope-intercept format:
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A.y-4=(x+2)
y=(x+2)+4
y = x + 6
B.y+4=(x-2)
y= x - 6
C.y+2=(x-4)
y = x - 6
D.y-2=(x+4)
y = x + 6
None of these lines have a slope of (2/5). In fact, only two even intersect point (-2,4):
A. y-4= (x+2) and
D. y-2 = (x+4)