What is the y-intercept of the line that is parallel to 2x + 3y = 4 and contains the point (6, -2)?

Answer 1

the given equation is,

#2x+3y=4#
or, #y=-2/3x +4/3#
now,let the equation of the line required be #y=mx+c#,where, #m# is the slope and #c# is the intercept.
Now,for both the lines to be parallel,slopes must be the same,so we get, #m=-2/3#
So,the equation of the line becomes, #y=-2/3x+c#
Now,given that the line passes through point #(6,-2)#,so putting in the equation we get,
#-2=(-2/3)*6+c#
or, #c=2#
And the equation becomes, #y=-2/3 x+2# graph{y=-2/3x+2 [-10, 10, -5, 5]}
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Answer 2

To find the y-intercept of the line parallel to (2x + 3y = 4) and passing through the point ((6, -2)), first, find the slope of the given line. Then, use the point-slope form of the equation to find the y-intercept.

  1. Convert the given equation to slope-intercept form: (y = mx + b), where (m) is the slope and (b) is the y-intercept. [2x + 3y = 4] [3y = -2x + 4] [y = -\frac{2}{3}x + \frac{4}{3}]

  2. The slope of the given line is (-\frac{2}{3}).

  3. Since the line we're looking for is parallel, it will have the same slope.

  4. Use the point-slope form of the equation: (y - y_1 = m(x - x_1)), where ((x_1, y_1)) is the given point and (m) is the slope. [y - (-2) = -\frac{2}{3}(x - 6)] [y + 2 = -\frac{2}{3}(x - 6)]

  5. To find the y-intercept, let (x = 0) and solve for (y): [y + 2 = -\frac{2}{3}(0 - 6)] [y + 2 = -\frac{2}{3}(-6)] [y + 2 = 4] [y = 4 - 2] [y = 2]

Therefore, the y-intercept of the line parallel to (2x + 3y = 4) and passing through the point ((6, -2)) is (2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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