Final answer:
To determine the slope and y-intercept of a linear equation, one can use different methods, including the point-slope form, slope-intercept form, or calculating the rise over run. The coefficient of x is the slope and the constant term is the y-intercept in the equation y = a + bx.
Step-by-step explanation:
There are multiple ways to determine the slope and y-intercept of a linear equation. One can use the point-slope form, convert the equation to slope-intercept form, or utilize the concept of finding the rise over run between two points on the line. Considering an equation in slope-intercept form, such as y = a + bx, the coefficient b represents the slope, indicating the steepness of the line, while the constant a represents the y-intercept, which is the point where the line crosses the y-axis.
For example, given a line with the equation y = 9 + 3x, the slope (m) is 3, as this line rises 3 units for each single unit increase along the x-axis. The y-intercept (b) is 9, meaning the line intersects the y-axis at the point (0,9). Understanding these components allows one to graph the linear relationship or predict how the line will behave.