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4.(06.02 MC)
The equation of line AB is y = 2x + 4. Write an equation of a line parallel to line AB In slope-Intercept form that contains point (3,-2). (4 points)
O y = 2x + 4
O y = 2x - 8

40602 MC The Equation Of Line AB Is Y 2x 4 Write An Equation Of A Line Parallel To Line AB In SlopeIntercept Form That Contains Point 32 4 Points O Y 2x 4 O Y 2 class=

Sagot :

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Answer:

The equation of a parallel line in the slope-Intercept form that contains the point (3,-2) is:

  • y = 2x- 8

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

Given the equation of a line

y = 2x + 4

comparing with the slope-intercept form of the line equation

The slope of the line AB is m = 2

We know that the parallel lines have the same slope.

Thus, the slope of the new line is also 2.

now we have,

  • The slope of new line m = 2
  • The point = (3, -2)

Using the point-slope form of the line equation

[tex]y-y_1=m\left(x-x_1\right)[/tex]

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 2 and the point (x₁, y₁) =  (3, -2)

[tex]y-y_1=m\left(x-x_1\right)[/tex]

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

y + 2 = 2x - 6

subtracting 2 from both sides

y + 2 - 2 = 2x - 6 - 2

y = 2x- 8

Therefore, the equation of a parallel line in the slope-Intercept form that contains the point (3,-2) is:

  • y = 2x- 8
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