How do you write an equation in point slope and slope intercept form given (8, -2) and perpendicular to the line whose equation is x-5y-7=0?
Point slope form equation:
Slope intercept form equation:
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To write the equation of a line in point-slope form and slope-intercept form, perpendicular to the line (x - 5y - 7 = 0) and passing through the point (8, -2), follow these steps:
- Convert the given equation (x - 5y - 7 = 0) into slope-intercept form (y = mx + b).
- Find the slope of the given line.
- Determine the slope of the line perpendicular to the given line.
- Use the point-slope form (y - y_1 = m(x - x_1)) with the given point (8, -2) and the perpendicular slope to find the equation in point-slope form.
- Convert the equation from point-slope form to slope-intercept form.
Let's solve it step by step:
- Convert the given equation (x - 5y - 7 = 0) to slope-intercept form:
[x - 5y - 7 = 0] [x - 7 = 5y] [y = \frac{1}{5}x - \frac{7}{5}]
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The slope of the given line is (m = \frac{1}{5}).
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The slope of the line perpendicular to the given line is the negative reciprocal of the slope of the given line. So, the perpendicular slope is (m_{\text{perpendicular}} = -\frac{1}{m} = -\frac{5}{1} = -5).
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Using the point-slope form with the given point (8, -2) and the perpendicular slope:
[y - (-2) = -5(x - 8)] [y + 2 = -5x + 40]
- Convert the equation to slope-intercept form:
[y = -5x + 40 - 2] [y = -5x + 38]
So, the equation of the line in both point-slope form and slope-intercept form, perpendicular to the line (x - 5y - 7 = 0) and passing through the point (8, -2), is:
Point-slope form: (y + 2 = -5(x - 8))
Slope-intercept form: (y = -5x + 38)
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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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