Reed Harris
02/22/2024 · Primary School
For each linear equation, identify the slope (m) and the y -intercept (b) a. \( y=4 x-5 \) b. \( y=11+\frac{2}{3} x \) c. \( y=\frac{2}{3} x \)
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Step-by-step Solution
To identify the slope (m) and the y-intercept (b) for each linear equation, we can compare them to the slope-intercept form of a linear equation, which is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
Let's analyze each equation:
a. \( y = 4x - 5 \)
- Slope (m): 4
- y-intercept (b): -5
b. \( y = 11 + \frac{2}{3}x \)
To express this in the standard form, we can rewrite it as:
\[ y = \frac{2}{3}x + 11 \]
- Slope (m): \(\frac{2}{3}\)
- y-intercept (b): 11
c. \( y = \frac{2}{3}x \)
This is already in slope-intercept form:
- Slope (m): \(\frac{2}{3}\)
- y-intercept (b): 0 (since there is no constant term)
In summary:
- a: \( m = 4, b = -5 \)
- b: \( m = \frac{2}{3}, b = 11 \)
- c: \( m = \frac{2}{3}, b = 0 \)
Quick Answer
a: \( m = 4, b = -5 \)
b: \( m = \frac{2}{3}, b = 11 \)
c: \( m = \frac{2}{3}, b = 0 \)
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