graph the line. \$y = 2x + 3\$

QUESTION IMAGE

$graph the line. \$y = 2x + 3\$$

Question

graph the line.

\$y = 2x + 3\$

Explanation:

Response

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Identify the y-intercept

\[

\begin{aligned} &\text{Equation: } y = 2x + 3\\ &\text{Form: } y = mx + b\\ &b = 3 \implies (0, 3) \end{aligned}

\]

Find a second point using the slope

\[

\begin{aligned} &m = 2 = \frac{\text{rise}}{\text{run}} = \frac{2}{1}\\ &x_2 = 0 + 1 = 1\\ &y_2 = 3 + 2 = 5 \implies (1, 5) \end{aligned}

\]

Verify with another point

\[

\begin{aligned} &x = -1\\ &y = 2(-1) + 3 = 1 \implies (-1, 1) \end{aligned}

\]
</reasoning>

<answer>
To graph the line $y = 2x + 3$, plot the y-intercept at $(0, 3)$ and use the slope of $2$ to plot a second point at $(1, 5)$ or $(-1, 1)$, then draw a straight line passing through these points.
</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[0, 3]],
"properties": {
"name": "y-intercept (0, 3)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "point",
"params": [[1, 5]],
"properties": {
"name": "(1, 5)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "line",
"params": [[0, 3], [1, 5]],
"properties": {
"strokeColor": "#5583F2",
"strokeWidth": 3
}
}
]
}
</plot>

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Answer: