Question

find the x and y intercepts of this linear equation.

\\4x + 8y = 64\\

x-intercept ( ? , )
y-intercept ( , )

Explanation:

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<reasoning>

Define intercepts on coordinate plane

Using the Coordinate Plane and Ordered Pairs knowledge points

• The \(x\)-intercept occurs where the line crosses the \(x\)-axis, meaning \(y = 0\). It is written as \((x, 0)\).
• The \(y\)-intercept occurs where the line crosses the \(y\)-axis, meaning \(x = 0\). It is written as \((0, y)\).

Calculate the x-intercept

Using the Linear Equations knowledge point
\[

$$\begin{aligned} 4x + 8(0) &= 64 \\ 4x &= 64 \\ x &= 16 \end{aligned}$$

\]
The \(x\)-intercept is \((16, 0)\).

Calculate the y-intercept

Using the Linear Equations knowledge point
\[

$$\begin{aligned} 4(0) + 8y &= 64 \\ 8y &= 64 \\ y &= 8 \end{aligned}$$

\]
The \(y\)-intercept is \((0, 8)\).
</reasoning>

<answer>
Find the \(x\) and \(y\) intercepts of this linear equation.

\[4x + 8y = 64\]

\(x\)-intercept <blank>\((16, 0)\)</blank>
\(y\)-intercept <blank>\((0, 8)\)</blank>
</answer>

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"type": "line",
"params": [[16, 0], [0, 8]],
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"name": "(16, 0)",
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"params": [[0, 8]],
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Answer:

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<reasoning>

Define intercepts on coordinate plane

Using the Coordinate Plane and Ordered Pairs knowledge points

• The \(x\)-intercept occurs where the line crosses the \(x\)-axis, meaning \(y = 0\). It is written as \((x, 0)\).
• The \(y\)-intercept occurs where the line crosses the \(y\)-axis, meaning \(x = 0\). It is written as \((0, y)\).

Calculate the x-intercept

Using the Linear Equations knowledge point
\[

$$\begin{aligned} 4x + 8(0) &= 64 \\ 4x &= 64 \\ x &= 16 \end{aligned}$$

\]
The \(x\)-intercept is \((16, 0)\).

Calculate the y-intercept

Using the Linear Equations knowledge point
\[

$$\begin{aligned} 4(0) + 8y &= 64 \\ 8y &= 64 \\ y &= 8 \end{aligned}$$

\]
The \(y\)-intercept is \((0, 8)\).
</reasoning>

<answer>
Find the \(x\) and \(y\) intercepts of this linear equation.

\[4x + 8y = 64\]

\(x\)-intercept <blank>\((16, 0)\)</blank>
\(y\)-intercept <blank>\((0, 8)\)</blank>
</answer>

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"strokeColor": "#F2557F",
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"type": "point",
"params": [[0, 8]],
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