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03/25/2024 · Middle School
rite an equation of the line with slope 5 and passing through \( (-1,5) \). Write the equation in standard form.
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Step-by-step Solution
To find the equation of a line with a given slope and passing through a specific point, we can use the point-slope form of the equation of a line:
\[ y - y_1 = m(x - x_1) \]
where:
- \( m \) is the slope of the line
- \( (x_1, y_1) \) is a point on the line
Given that the slope \( m = 5 \) and the point \( (-1, 5) \), we can substitute these values into the point-slope form to find the equation of the line.
Substitute \( m = 5 \), \( x_1 = -1 \), and \( y_1 = 5 \) into the point-slope form:
\[ y - 5 = 5(x - (-1)) \]
\[ y - 5 = 5(x + 1) \]
\[ y - 5 = 5x + 5 \]
\[ y = 5x + 10 \]
Therefore, the equation of the line with slope 5 and passing through \( (-1, 5) \) in standard form is \( y = 5x + 10 \).
Quick Answer
The equation of the line is \( y = 5x + 10 \).
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