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What is the equation of the line in slope-intercept form that passes through point (0, −2) and is parallel to the line y = negative one halfx + 6? Show all necessary steps



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nuhulawal20

The equation of the line that passes through the given point and is parallel to the given line is y = -(1/2)x - 2

What is the equation of the line  that passes through the given point and is parallel to the given line?

Given the data in the question;

  • y = -(1/2)x + 6
  • Point: (0, −2)

Since the equation is already in slope intercept form, compare with slope intercept formula to determine the slope and y-intercept. y = mx + b.

y = -(1/2)x + 6

y = mx + b

Slope m = -(1/2)

b = 6

Now, to determine the equation parallel, the slopes must equal.

We can do this using the point-slope formula.

y - y₁ = m( x - x₁ )

Substitute Slope m -(1/2) and point (0, −2) into the formula

y - (-2) = -(1/2)( x - 0 )

y + 2 = -(1/2)x

y = -(1/2)x - 2

Therefore, the equation of the line that passes through the given point and is parallel to the given line is y = -(1/2)x - 2

Learn more about slope formula here: https://brainly.com/question/24368732

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