Expressions, Equations, and Relationships>Representing Linear Relationships with Tables, Graphs, and Equations(TEKS.Math.7.7)
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Texas 7th Grade Math › Expressions, Equations, and Relationships>Representing Linear Relationships with Tables, Graphs, and Equations(TEKS.Math.7.7)
Which equation represents this table?
x: -1, 0, 1, 3 y: -5, -3, -1, 3
$y = 2x + 3$
$y = x - 3$
$y = -2x - 3$
$y = 2x - 3$
Explanation
From the table, as $x$ increases by 1, $y$ increases by 2, so $m=2$. When $x=0$, $y=-3$, so $b=-3$. The equation is $y=2x-3$. Check: for $x=3$, $y=2(3)-3=3$, matching the table.
Which table matches $y = -\frac{1}{2}x + 4$?
x: 0, 2, 4, 8; y: 4, 5, 6, 8
x: 0, 2, 4, 8; y: 4, 3, 2, 0
x: 0, 2, 4, 8; y: 5, 4, 3, 1
x: 0, 2, 4, 8; y: 4, 2, 0, -4
Explanation
The slope is $m=-\tfrac{1}{2}$, so for every increase of 2 in $x$, $y$ decreases by 1. The intercept is $b=4$, so when $x=0$, $y=4$. Only the table in choice B has $y=4$ at $x=0$ and then 3, 2, 0 as $x$ goes 2, 4, 8.
Which equation represents this table?
x: -1, 0, 1, 2 y: 5, 2, -1, -4
$y = -3x + 2$
$y = 3x + 2$
$y = -3x - 2$
$y = -2x + 2$
Explanation
As $x$ increases by 1, $y$ decreases by 3, so $m=-3$. When $x=0$, $y=2$, so $b=2$. Therefore the equation is $y=-3x+2$.
Which table matches $y = \frac{3}{4}x - 2$?
x: 0, 4, 8, 12; y: 2, 5, 8, 11
x: 0, 4, 8, 12; y: -2, -5, -8, -11
x: 0, 4, 8, 12; y: -2, 1, 4, 7
x: 0, 4, 8, 12; y: -2, 2, 6, 10
Explanation
The slope is $m=\tfrac{3}{4}$ and intercept is $b=-2$. At $x=0$, $y=-2$. Increasing $x$ by 4 increases $y$ by $3$. Choice C shows $y=-2, 1, 4, 7$ for $x=0,4,8,12$, matching $y=\tfrac{3}{4}x-2$.
Which equation represents this table?
x: -2, 0, 2, 6 y: -6, -5, -4, -2
$y = \tfrac{1}{2}x - 5$
$y = \tfrac{1}{2}x + 5$
$y = -\tfrac{1}{2}x - 5$
$y = \tfrac{3}{2}x - 5$
Explanation
From the table, when $x$ increases by 2, $y$ increases by 1, so $m=\tfrac{1}{2}$. When $x=0$, $y=-5$, so $b=-5$. Thus the equation is $y=\tfrac{1}{2}x-5$.