The image shows line p. For each equation below, decide whether the line it represents is parallel to line p, perpendicular to line p, or neither of these.y=−3x+10neithery−5=−(31)(x+2)[Select]y=31x[Select]−3x+y=1[Select]
Q. The image shows line p. For each equation below, decide whether the line it represents is parallel to line p, perpendicular to line p, or neither of these.y=−3x+10neithery−5=−(31)(x+2)[Select]y=31x[Select]−3x+y=1[Select]
Determine Slope of Line: Determine the slope of line p from the given equation y=−3x+10. Comparing this with the standard form y=mx+b, we identify the slope (m) of line p as −3.
Analyzing Equation y−5: Analyze the equation y−5=−31(x+2). First, simplify it to slope-intercept form: y=−31x−31⋅2+5, which simplifies to y=−31x+431. The slope here is −31. Since the slopes −3 and −31 are not equal nor opposite reciprocals, this line is neither parallel nor perpendicular to line p.
Consider Equation y=(31)x: Consider the equation y=(31)x. The slope here is 31. Since 31 is not equal to −3 and also not the negative reciprocal of −3, this line is neither parallel nor perpendicular to line p.
Examine Equation −3x+y: Examine the equation −3x+y=1. Rearrange it to slope-intercept form: y=3x+1. The slope here is 3. Since 3 is not equal to −3 and is not the negative reciprocal of −3, this line is neither parallel nor perpendicular to line p.
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