Graph: [tex]y-3=\frac{1}{2}(x+2)[/tex]
What is the [tex]y[/tex]-intercept of the graphed linear function?
(0,-8)
(0,-2)
(0,2)
(0,4)
The correct line is shown.
Answer (2)
Substitute x = 0 into the equation y − 3 = 2 1 ( x + 2 ) .
Simplify the equation: y − 3 = 2 1 ( 0 + 2 ) = 1 .
Solve for y : y = 1 + 3 = 4 .
The y -intercept is ( 0 , 4 ) .
Explanation
Understanding the Problem We are given the equation of a line: y − 3 = 2 1 ( x + 2 ) . We want to find the y -intercept of this line. The y -intercept is the point where the line crosses the y -axis, which means the x -coordinate of this point is 0.
Substituting x=0 To find the y -intercept, we substitute x = 0 into the equation of the line: y − 3 = 2 1 ( 0 + 2 ) .
Solving for y Now, we simplify the equation and solve for y :
y − 3 = 2 1 ( 2 )
y − 3 = 1
y = 1 + 3
y = 4
Finding the y-intercept Therefore, the y -intercept is the point ( 0 , 4 ) .
Examples
Understanding the y-intercept of a line is useful in many real-world scenarios. For example, if you are tracking the cost of a taxi ride, the y-intercept represents the initial fee or the cost when the distance traveled is zero. Similarly, in a savings account, the y-intercept could represent the initial deposit before any interest is earned. Knowing the y-intercept helps in interpreting the starting point or initial condition in various linear relationships.
The y -intercept of the given linear function is the point ( 0 , 4 ) . We find this by substituting x = 0 into the equation and solving for y . Thus, the correct answer is ( 0 , 4 ) .
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