Questions: Which ordered pairs are on the line with equation (y-0.75=1.25(x-3))? Select each correct answer. ((4,2)) ((1,1.75)) ((7,5.5)) ((-4,-8))

Which ordered pairs are on the line with equation (y-0.75=1.25(x-3))? Select each correct answer. ((4,2)) ((1,1.75)) ((7,5.5)) ((-4,-8))
Transcript text: Which ordered pairs are on the line with equation $y-0.75=1.25(x-3)$ ? Select each correct answer. $(4,2)$ $(1,1.75)$ $(7,5.5)$ $(-4,-8)$
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Solution

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Solution Steps

Step 1: Convert the Equation to Slope-Intercept Form

The given equation is:

\[ y - 0.75 = 1.25(x - 3) \]

To convert this to the slope-intercept form \(y = mx + b\), we first distribute the 1.25 on the right side:

\[ y - 0.75 = 1.25x - 3.75 \]

Next, add 0.75 to both sides to solve for \(y\):

\[ y = 1.25x - 3.75 + 0.75 \]

Simplify the equation:

\[ y = 1.25x - 3 \]

Step 2: Check Each Ordered Pair

We will substitute each ordered pair into the equation \(y = 1.25x - 3\) to see if it satisfies the equation.

Pair 1: \((4, 2)\)

Substitute \(x = 4\) and \(y = 2\):

\[ 2 = 1.25(4) - 3 \]

Calculate the right side:

\[ 2 = 5 - 3 \]

\[ 2 = 2 \]

The pair \((4, 2)\) satisfies the equation.

Pair 2: \((1, 1.75)\)

Substitute \(x = 1\) and \(y = 1.75\):

\[ 1.75 = 1.25(1) - 3 \]

Calculate the right side:

\[ 1.75 = 1.25 - 3 \]

\[ 1.75 = -1.75 \]

The pair \((1, 1.75)\) does not satisfy the equation.

Pair 3: \((7, 5.5)\)

Substitute \(x = 7\) and \(y = 5.5\):

\[ 5.5 = 1.25(7) - 3 \]

Calculate the right side:

\[ 5.5 = 8.75 - 3 \]

\[ 5.5 = 5.75 \]

The pair \((7, 5.5)\) does not satisfy the equation.

Pair 4: \((-4, -8)\)

Substitute \(x = -4\) and \(y = -8\):

\[ -8 = 1.25(-4) - 3 \]

Calculate the right side:

\[ -8 = -5 - 3 \]

\[ -8 = -8 \]

The pair \((-4, -8)\) satisfies the equation.

Final Answer

The ordered pairs that are on the line are:

\[ \boxed{(4, 2)} \] \[ \boxed{(-4, -8)} \]

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