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МатематикаВопрос:
Given the line y = 2x + b, and point A(-1, -5). Find b.
Ответ:
Linear Equation with a Point:
- Equation: y = 2x + b
- Point A: (-1, -5)
Brief explanation: To find the value of 'b' (the y-intercept), we substitute the coordinates of the given point into the equation of the line and solve for 'b'.
Step-by-step solution:
- Step 1: Substitute the coordinates of point A into the equation.
The coordinates of point A are x = -1 and y = -5.
Substitute these values into y = 2x + b:
\[ -5 = 2(-1) + b \] - Step 2: Simplify the equation.
\[ -5 = -2 + b \] - Step 3: Solve for b.
Add 2 to both sides of the equation:
\[ -5 + 2 = b \]
\[ -3 = b \]
Answer: b = -3
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