Answer: D. (5, 4)
Step-by-step explanation:
An x-intercept of -1 means the point = (-1, 0)
So find the slope(m) using the formula: [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex](x_{1},y_{1})=(-4,-2)\\(x_{2},y_{2})=(-1,0)\\\\m = \frac{0-(-2)}{-1-(-4)}=\frac{0+2}{4-1}=\frac{2}{3}[/tex]
Now find the y-intercept(b) by substituting a point into the function:
y = mx + b
[tex]y=\frac{2}{3} x+b\\\\0=\frac{2}{3} (-1)+b\\\\0=-\frac{2}{3}+b\\\\b=\frac{2}{3}[/tex]
So now the function is determined as [tex]y=\frac{2}{3} x+\frac{2}{3}=\frac{2}{3}(x+1)[/tex].
Bring each of the coordinates in to see if it fits in:
A. (-6, -5) [tex]\frac{2}{3}(-6+1)=\frac{2}{3}(-5)=-3.33\neq -5[/tex]
B. (3, 2) [tex]\frac{2}{3}(3+1)=\frac{2}{3}(4)=2.67\neq 2[/tex]
C. (4, 5) [tex]\frac{2}{3}(4+1)=\frac{2}{3}(5)=3.33\neq 5[/tex]
D. (5, 4) [tex]\frac{2}{3}(5+1)=\frac{2}{3}(6)=4[/tex]
