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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Step-by-step Solution
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:
\[
y = -\frac{3}{4}x + 2
\]
Quick Answer
\( y = -\frac{3}{4}x + 2 \)
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