Question

A coordinate plane.

A line goes through the point (–4,–2) and has an x-intercept of –1.
Which point also lies on the line?
A (–6,–5)
B (3,2)
C (4,5)
D (5,4)

Answer 1

D(5,4)

Explanation:

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Answer 2

Answer: D. (5, 4)

Explanation:

An x-intercept of -1 means the point = (-1, 0)

So find the slope(m) using the formula:
`(y_(2)-y_(1))/(x_(2)-x_(1))`

`(x_(1),y_(1))=(-4,-2)\\(x_(2),y_(2))=(-1,0)\\\\m = (0-(-2))/(-1-(-4))=(0+2)/(4-1)=(2)/(3)`

Now find the y-intercept(b) by substituting a point into the function:

y = mx + b

`y=(2)/(3) x+b\\\\0=(2)/(3) (-1)+b\\\\0=-(2)/(3)+b\\\\b=(2)/(3)`

So now the function is determined as
`y=(2)/(3) x+(2)/(3)=(2)/(3)(x+1)`.

Bring each of the coordinates in to see if it fits in:

A. (-6, -5)
`(2)/(3)(-6+1)=(2)/(3)(-5)=-3.33\\eq -5`

B. (3, 2)
`(2)/(3)(3+1)=(2)/(3)(4)=2.67\\eq 2`

C. (4, 5)
`(2)/(3)(4+1)=(2)/(3)(5)=3.33\\eq 5`

D. (5, 4)
`(2)/(3)(5+1)=(2)/(3)(6)=4`