Question
Write an equation for the line described. Give the answer in standard form. through \( (1,4), \mathrm{m}=-4 \) The equation of the line is (Type your answer in standard form.)
Ask by Marsh Hodgson. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equation of the line in standard form is \(4x + y = 8\).
Solution
To find the equation, start with the point-slope form:
y - 4 = -4(x - 1)
Expand:
y - 4 = -4x + 4
Add 4 to both sides:
y = -4x + 8
Now, write in standard form (Ax + By = C):
4x + y = 8
Thus, the equation of the line in standard form is 4x + y = 8.
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Simplify this solution Bonus Knowledge
To find the equation of the line in standard form, we start with the point-slope formula: \( y - y_1 = m(x - x_1) \). Substituting in the point \( (1,4) \) and the slope \( m = -4 \), we have: \[ y - 4 = -4(x - 1) \] Expanding this gives: \[ y - 4 = -4x + 4 \] Adding 4 to both sides leads to: \[ y = -4x + 8 \] To convert this into standard form \( Ax + By = C \), we rearrange it: \[ 4x + y = 8 \] So, the equation of the line in standard form is: \[ 4x + y = 8 \]
