The y-intercept of a linear equation is found by setting x to zero and solving for y. The term b or a in the equation y = mx + b or y = a + bx represents the y-intercept.
This point shows where the line crosses the y-axis and describes the y-value when x is zero.
To find the y-intercept of a linear equation, such as y = mx + b or y = a + bx, you set the x-value to zero and solve for y.
The term b or a in these equations represents the y-intercept, which indicates the point where the line crosses the y-axis.
This intercept gives you the value of y when x equals zero.
However, it is important to note that sometimes in the context of the problem, a y-intercept at x = 0 may not make practical sense, such as predicting a test score (y) when there was no test taken (x = 0).
For example, if the equation of a line is y = -266.8863 + 0.1656x, the y-intercept is -266.8863, which is the y-value when x is 0.
The slope of the line, indicated by the coefficient of x (0.1656 in this example), describes the steepness of the line.
If a line has a larger y-intercept, this would graphically shift the line up, while a smaller y-intercept would shift it down.
When working within models, such as those used in economics, different intercepts and slopes can alter the predictions based on the model equations.