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Identify the equation of the line with s...

Identify the equation of the line with slope = - 4 and y-intercept = 2.

A

`2x + (y)/(2) =1 `

B

`2x +(y)/(3) =1 `

C

2x+y=1

D

`2x +(y)/(4)=1 `

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To find the equation of the line with a given slope and y-intercept, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the slope (m) and y-intercept (c)**: - The slope (m) is given as -4. - The y-intercept (c) is given as 2. 2. **Write the general equation of a line**: - The equation of a line in slope-intercept form is given by: \[ y = mx + c \] 3. **Substitute the values of m and c into the equation**: - Substitute \( m = -4 \) and \( c = 2 \) into the equation: \[ y = -4x + 2 \] 4. **Rearranging the equation (if necessary)**: - We can rearrange the equation to isolate y: \[ y + 4x = 2 \] 5. **Divide the entire equation by 2 (optional)**: - To simplify, we can divide the whole equation by 2: \[ \frac{y}{2} + 2x = 1 \] 6. **Final equation**: - The final equation of the line can be expressed as: \[ \frac{y}{2} + 2x = 1 \] ### Summary: The equation of the line with slope -4 and y-intercept 2 is: \[ \frac{y}{2} + 2x = 1 \]
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