The equation y=4 represents a linear function because it is a horizontal line, indicating a constant y-value for any x-value. The equation x=4 does not represent a linear function, as it is a vertical line and cannot be expressed in the form y = a + bx.
Linear Equations and Their Graphs
Let's consider the two equations given:
y=4 is a horizontal line on the graph because it does not change as x changes. It shows that for any value of x, y will always be 4. This represents a linear function, because it can be written in the form y = a + bx, where a is the y-intercept and b is the slope which is 0 in this case.
x=4 is a vertical line on the graph. Every point on this line has an x-coordinate of 4. However, this is not a function, linear or otherwise, because it does not have a unique y-value for every x-value and therefore cannot be written in the form y = a + bx.
For example, the equation y = x + 4 is linear because it has the form y = a + bx, just like the example provided in the question. It shows a direct, linear relationship between x and y, and when graphed, it produces a straight line with a slope (b) of 1 and a y-intercept (a) of 4.