Final answer:
To find the y-intercept of a line, set x to zero in the equation and solve for y; it’s the point where the line crosses the y-axis. The slope is the rate of increase of y with respect to x. For the x-intercept, set y to zero and solve for x; it’s where the line crosses the x-axis.
Step-by-step explanation:
To find the y-intercept and the x-intercept of a line, one must understand the role of independent and dependent variables in a linear equation. In a typical linear equation of the form y = mx + b, m represents the slope, and b represents the y-intercept. The slope indicates the rate of change of the dependent variable with respect to the independent variable, while the y-intercept is the value of y where the line crosses the y-axis, typically when x is zero.
The independent variable is the variable we have control over or that we can change - often represented as x. The dependent variable, often represented by y, is the variable that depends on the value of the independent variable.
To find the y-intercept of the equation y = 55x + 75, for example, we set x to zero and solve for y. The y-intercept is 75, which means that if no hours are worked on a car (x=0), the total labor charge (y) starts at $75. Similarly, the slope in this equation is 55, which represents the rate at which labor charges increase per hour worked.
In another example, an equation like y = 3x + 9 has a y-intercept of 9, indicating the point (0,9) on the graph, and a slope of 3. This means for every incremental increase of 1 in x, the value of y increases by 3. The x-intercept here can be found by setting y to zero and solving for x, resulting in x to be -3.