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Consider the line y= -3/2x-8 . Find the equation of the line that is parallel to this line and passes through the point (-2,3). Find the equation of the line and passes through the point (-2,3)

User LightBulb
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Answer:

The given line has a slope of -3/2, since it is in the form y = mx + b, where m is the slope. Any line that is parallel to this line will also have a slope of -3/2.

To find the equation of the line that passes through the point (-2,3) and has a slope of -3/2, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope. Substituting in the values we have:

y - 3 = (-3/2)(x - (-2))

y - 3 = (-3/2)x - 3

y = (-3/2)x - 3 + 3

y = (-3/2)x

Therefore, the equation of the line that is parallel to y = -3/2x - 8 and passes through the point (-2,3) is y = (-3/2)x.

Note that this line does not have a y-intercept, since it passes through the point (-2,3) and has a slope of -3/2.

User Jeka
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