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\( \begin{array}{l}\text { Which of the following points lies on the line represented by the equation } \\ y-2=3(x+1) \text { ? point }\end{array} \) \( \begin{array}{l}(-2,8) \\ (-1,2) \\ (0,5)\end{array} \) submit Clear selection Slear form

Ask by Hills Hill. in the United States
Jan 21,2025

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The points \((-1, 2)\) and \((0, 5)\) lie on the line.

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Beyond the Answer

To find out which point lies on the line represented by the equation \( y - 2 = 3(x + 1) \), let's first rearrange it into slope-intercept form. Distributing on the right side gives us \( y - 2 = 3x + 3 \), which simplifies to \( y = 3x + 5 \). Now we can test each point. 1. For the point \((-2, 8)\): \( y = 3(-2) + 5 = -6 + 5 = -1 \) (not a match). 2. For the point \((-1, 2)\): \( y = 3(-1) + 5 = -3 + 5 = 2 \) (match!). 3. For the point \((0, 5)\): \( y = 3(0) + 5 = 0 + 5 = 5 \) (match!). So, the points \((-1, 2)\) and \((0, 5)\) lie on the line, but \((-2, 8)\) does not. The correct answer is the point \((-1, 2)\)! Now are you ready for some engaging background? The line equation \(y - 2 = 3(x + 1)\) is in point-slope form, which is handy when you know a point on the line and its slope! This form arose from the idea of measuring the steepness of a line which has been crucial in understanding the graphing of linear equations. Need tips for similar problems? Remember to always convert your equations to the familiar \(y = mx + b\) format. This will make it easier to identify points that satisfy the equation and spot common mistakes like incorrect arithmetic or misinterpreting the slope. Happy graphing!

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