To determine whether each point lies on the graph of the equation [tex]\( 4x - y - 5 = 0 \)[/tex], we will substitute the coordinates of each point into the equation and check if the equation holds true (i.e., whether it equals zero).
(a) Point (1, 2)
Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = 2 \)[/tex] into the equation:
[tex]\[
4(1) - 2 - 5
\][/tex]
First, calculate [tex]\( 4 \times 1 \)[/tex]:
[tex]\[
4
\][/tex]
Next, subtract [tex]\( 2 \)[/tex]:
[tex]\[
4 - 2 = 2
\][/tex]
Finally, subtract [tex]\( 5 \)[/tex]:
[tex]\[
2 - 5 = -3
\][/tex]
The equation does not equal zero ([tex]\(-3 \neq 0\)[/tex]). Therefore, the point [tex]\((1, 2)\)[/tex] is not on the graph.
(b) Point (1, -1)
Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = -1 \)[/tex] into the equation:
[tex]\[
4(1) - (-1) - 5
\][/tex]
First, calculate [tex]\( 4 \times 1 \)[/tex]:
[tex]\[
4
\][/tex]
Next, add [tex]\( 1 \)[/tex] (since subtracting a negative is equivalent to adding):
[tex]\[
4 + 1 = 5
\][/tex]
Finally, subtract [tex]\( 5 \)[/tex]:
[tex]\[
5 - 5 = 0
\][/tex]
The equation equals zero ([tex]\(0 = 0\)[/tex]). Therefore, the point [tex]\((1, -1)\)[/tex] is on the graph.
Summary:
(a) [tex]\((1, 2)\)[/tex] - No, the point is not on the graph.
(b) [tex]\((1, -1)\)[/tex] - Yes, the point is on the graph.
