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Determine whether the given points are on the graph of [tex]y = 2x + 3[/tex].

Select all points that lie on the graph.

A. [tex](-1, 1)[/tex]
B. [tex](-4, -6)[/tex]
C. [tex](0, -2)[/tex]
D. [tex](-2, -1)[/tex]

Sagot :

GinnyAnswer
To determine whether the given points lie on the graph of the linear function [tex]\( y = 2x + 3 \)[/tex], we will substitute the [tex]\( x \)[/tex]-coordinate of each point into the equation and check if the resulting [tex]\( y \)[/tex]-value matches the [tex]\( y \)[/tex]-coordinate of the point.

Let's analyze each point one by one:

### Point [tex]\((-1, 1)\)[/tex]

1. Substitute [tex]\( x = -1 \)[/tex] into the equation [tex]\( y = 2x + 3 \)[/tex]:
[tex]\[ y = 2(-1) + 3 = -2 + 3 = 1 \][/tex]

2. The [tex]\( y \)[/tex]-value we calculated is [tex]\( 1 \)[/tex], which matches the [tex]\( y \)[/tex]-coordinate of the point [tex]\((-1, 1)\)[/tex].

Thus, the point [tex]\((-1, 1)\)[/tex] lies on the graph.

### Point [tex]\((-4, -6)\)[/tex]

1. Substitute [tex]\( x = -4 \)[/tex] into the equation [tex]\( y = 2x + 3 \)[/tex]:
[tex]\[ y = 2(-4) + 3 = -8 + 3 = -5 \][/tex]

2. The [tex]\( y \)[/tex]-value we calculated is [tex]\( -5 \)[/tex], which does not match the [tex]\( y \)[/tex]-coordinate of the point [tex]\((-4, -6)\)[/tex].

Thus, the point [tex]\((-4, -6)\)[/tex] does not lie on the graph.

### Point [tex]\((0, -2)\)[/tex]

1. Substitute [tex]\( x = 0 \)[/tex] into the equation [tex]\( y = 2x + 3 \)[/tex]:
[tex]\[ y = 2(0) + 3 = 0 + 3 = 3 \][/tex]

2. The [tex]\( y \)[/tex]-value we calculated is [tex]\( 3 \)[/tex], which does not match the [tex]\( y \)[/tex]-coordinate of the point [tex]\((0, -2)\)[/tex].

Thus, the point [tex]\((0, -2)\)[/tex] does not lie on the graph.

### Point [tex]\((-2, -1)\)[/tex]

1. Substitute [tex]\( x = -2 \)[/tex] into the equation [tex]\( y = 2x + 3 \)[/tex]:
[tex]\[ y = 2(-2) + 3 = -4 + 3 = -1 \][/tex]

2. The [tex]\( y \)[/tex]-value we calculated is [tex]\( -1 \)[/tex], which matches the [tex]\( y \)[/tex]-coordinate of the point [tex]\((-2, -1)\)[/tex].

Thus, the point [tex]\((-2, -1)\)[/tex] lies on the graph.

### Conclusion

After checking each point, we find that the points [tex]\((-1, 1)\)[/tex] and [tex]\((-2, -1)\)[/tex] lie on the graph of the function [tex]\( y = 2x + 3 \)[/tex].
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