Mathematical Process Standards>Communicating Mathematical Ideas with Multiple Representations(TEKS.Math.7.1.D)
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Texas 7th Grade Math › Mathematical Process Standards>Communicating Mathematical Ideas with Multiple Representations(TEKS.Math.7.1.D)
Which equation matches this table? x: -2, 0, 1, 3; y: -1, 3, 5, 9
$y = 2x + 3$
$y = 3x + 2$
$y = 2x - 3$
$y = -2x + 3$
Explanation
When $x=0$, $y=3$, so $b=3$. From $x=0$ to $x=1$, $y$ increases from 3 to 5, a change of 2, so $m=2$. The matching equation is $y=2x+3$. The other choices change the slope or intercept.
Which equation matches this table? x: -2, 0, 2, 6; y: 7, 4, 1, -5
$y = 1.5x + 4$
$y = -x + 4$
$y = -1.5x + 4$
$y = -1.5x - 4$
Explanation
When $x=0$, $y=4$, so $b=4$. From $x=-2$ to $x=0$, $y$ changes from 7 to 4 (down 3) while $x$ increases by 2, so $m=\frac{-3}{2}=-1.5$. Thus $y=-1.5x+4$.
Which table matches $y = 2x - 6$?
x: 0, 3, 6, 9; y: -4, 2, 8, 14
x: 0, 3, 6, 9; y: -6, -12, -18, -24
x: 0, 3, 6, 9; y: 6, 12, 18, 24
x: 0, 3, 6, 9; y: -6, 0, 6, 12
Explanation
At $x=0$, $y=-6$ sets $b=-6$. Slope $m=2$ means each increase of 3 in $x$ raises $y$ by 6. The table with $y: -6, 0, 6, 12$ matches $y=2x-6$.
Which table matches $y = \frac{3}{4}x + 2$?
x: 0, 4, 8, 12; y: 2, 3, 4, 5
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, -1, -4, -7
Explanation
At $x=0$, $y=2$ gives $b=2$. With $m=\tfrac{3}{4}$, increasing $x$ by 4 increases $y$ by 3. The row $y: 2, 5, 8, 11$ fits $y=\frac{3}{4}x+2$.