Get detailed and accurate answers to your questions on IDNLearn.com. Join our knowledgeable community and access a wealth of reliable answers to your most pressing questions.
Sagot :
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.
(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.
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.