Question
Find the slope \( m \) and the \( y \)-intercept \( b \) of the line whose equation is given. \( 5 x-y=4 \)
Ask by Lawson Beck. in the United States
Feb 19,2025
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Answer
The slope \( m \) is 5 and the y-intercept \( b \) is -4.
Solution
To find the slope and y-intercept, we first rewrite the equation in slope-intercept form, y = mx + b.
Starting with:
5x - y = 4
Isolate y by subtracting 5x from both sides:
-y = 4 - 5x
Multiply both sides by -1:
y = 5x - 4
Now the equation is in the form y = mx + b, where:
m (slope) = 5
b (y-intercept) = -4
Thus, the slope is 5 and the y-intercept is -4.
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Simplify this solution Bonus Knowledge
To find the slope \( m \) and the \( y \)-intercept \( b \), we'll first rewrite the equation \( 5x - y = 4 \) in slope-intercept form, which is \( y = mx + b \). Starting with the original equation, we isolate \( y \): \[ -y = -5x + 4 \] Multiplying each term by -1 gives us: \[ y = 5x - 4 \] From this equation, we can easily identify the slope \( m \) and the \( y \)-intercept \( b \): - The slope \( m = 5 \) - The \( y \)-intercept \( b = -4 \) So, the slope is 5 and the \( y \)-intercept is -4.
