How do you write a slope-intercept equation for a line parallel to the line x-2y=6 which passes through the point (-5,2)?
then, the condition of they being parallel is
Then, the equation of parallel line will be
If it passes through the point (-5, 2), then the equation will be satisfied with these values.
The equation, at slope-intercept form is
graph{y = (x + 9)/2 [-20.27, 20.26, -10.14, 10.13]}
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"Rearrange x-2y=6 into this form"
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To write a slope-intercept equation for a line parallel to the line (x - 2y = 6) which passes through the point ((-5,2)):
- Rewrite the given equation in slope-intercept form: (y = mx + b), where (m) is the slope and (b) is the y-intercept.
- Determine the slope ((m)) of the given line.
- The slope of a line parallel to the given line will be the same.
- Use the point-slope form of a linear equation: (y - y_1 = m(x - x_1)), where ((x_1, y_1)) is the given point.
- Substitute the slope ((m)) and the coordinates of the given point into the point-slope form.
- Solve for (y) to obtain the slope-intercept equation.
Let's solve:
- Given equation: (x - 2y = 6)
Rewrite in slope-intercept form: (y = \frac{1}{2}x - 3) - Slope ((m)) of the given line is (\frac{1}{2}).
- Since the line we want is parallel, its slope is also (\frac{1}{2}).
- Using point-slope form with the given point ((-5,2)): (y - 2 = \frac{1}{2}(x + 5))
- Simplify: (y - 2 = \frac{1}{2}x + \frac{5}{2})
- (y = \frac{1}{2}x + \frac{5}{2} + 2)
(y = \frac{1}{2}x + \frac{9}{2})
So, the slope-intercept equation for the line parallel to (x - 2y = 6) passing through ((-5,2)) is (y = \frac{1}{2}x + \frac{9}{2}).
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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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