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Graph the following features: - Y-intercept \( =-4 \) - Slope \( =2 \)

Ask by Haynes Burton. in the United States
Feb 24,2025

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Answer

To graph the line: 1. Plot the y-intercept at (0, -4). 2. Use the slope of 2 to find another point: move right 1 unit and up 2 units to (1, -2). 3. Draw a straight line through these points. This line crosses the y-axis at -4 and rises 2 units for every 1 unit to the right.

Solution

We can start by writing the equation of the line using the slope‑intercept form:   y = mx + b Here, the slope m = 2 and the y‑intercept b = –4. So the equation is:   y = 2x – 4 To graph this line: 1. Plot the y‑intercept (0, –4) on the coordinate plane. 2. Use the slope to find another point. Since the slope is 2 (which means “rise over run” = 2/1), from (0, –4) move right 1 unit (x = 1) and up 2 units (y = –4 + 2 = –2). Mark the point (1, –2). 3. Draw a straight line through these two points to represent the equation y = 2x – 4. The resulting graph is a straight line that crosses the y‑axis at –4 and rises 2 units for every 1 unit it moves to the right.

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To graph the line with a Y-intercept of \(-4\) and a slope of \(2\), start by plotting the point \((0, -4)\) on the Y-axis. This is where your line crosses the Y-axis. Next, remember that a slope of \(2\) means for every \(1\) unit you move to the right (along the X-axis), you move \(2\) units up (along the Y-axis). From the point \((0, -4)\), move right to \((1, -2)\), then from there move to \((2, 0)\) to find another point. Draw a straight line through these points, and you’ve got your graph! To ensure your graph is accurate, it can be helpful to choose additional points along the line. For a slope of \(2\), you can also go down from \((0, -4)\) and move left: if you go left \(1\) unit to \((-1, -4)\), you can move down \(2\) units to \((-1, -6)\). Then, connect these points! Always double-check your slope by selecting any two points on the line and ensuring the rise over run equals \(2\). Happy graphing!

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