Alexander Collins
11/15/2023 · High School

1 point Find the equation of the line with the \( y \)-intercept 2 and passes through the point \( (4,-1) \), Answer: \( y= \) type your answer...

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To find the equation of the line with a \( y \)-intercept of 2 and passing through the point \( (4, -1) \), we can start by using the slope-intercept form of a line, which is given by: \[ y = mx + b \] where \( m \) is the slope and \( b \) is the \( y \)-intercept. Since the \( y \)-intercept is given as 2, we have: \[ b = 2 \] So the equation becomes: \[ y = mx + 2 \] Next, we need to find the slope \( m \). We can use the point \( (4, -1) \) to find the slope. The point can be substituted into the equation: \[ -1 = m(4) + 2 \] Now, we can solve for \( m \): \[ -1 = 4m + 2 \] \[ -1 - 2 = 4m \] \[ -3 = 4m \] \[ m = -\frac{3}{4} \] Now that we have the slope, we can write the complete equation of the line: \[ y = -\frac{3}{4}x + 2 \] Thus, the final answer is: \[ y = -\frac{3}{4}x + 2 \]

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\( y = -\frac{3}{4}x + 2 \)
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