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Use technology to find points and graph the line \( 4 x=-2 y+8 \), following the instructions below.

Ask by Ruiz Brooks. in the United States
Dec 19,2024

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To graph the line \( 4x = -2y + 8 \), rearrange it to \( y = -2x + 4 \). Plot points like \( (0, 4) \), \( (2, 0) \), and \( (-2, 8) \), then draw a straight line through them.

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The Deep Dive

To graph the equation \( 4x = -2y + 8 \), first, we can rearrange it into slope-intercept form \( y = mx + b \) by isolating \( y \). Rearranging gives us \( 2y = -4x + 8 \), or \( y = -2x + 4 \). Using technology, you can use a graphing calculator or graphing software like Desmos to plot this line. Simply enter the equation \( y = -2x + 4 \) and observe the slope of -2 and the y-intercept at 4! Once you have the line graphed, you can also find at least two points on the line for added clarity. For instance, when \( x = 0 \), \( y = 4 \) (the y-intercept), and for \( x = 2 \), \( y = 0 \) (the x-intercept). You can plot these points along with the line to see how they intersect, making it easier to visualize the relationship represented by the equation!

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