Final answer:
The slope-intercept form of a linear equation is y = mx + b, where 'm' is the slope and 'b' is the y-intercept. The slope indicates the rise over run, and the y-intercept is where the line crosses the y-axis. For a line with a slope of 3 and a y-intercept of 9, the equation is y = 3x + 9.
Step-by-step explanation:
The slope-intercept form of a linear equation is commonly written as y = mx + b. In this equation, 'm' represents the slope of the line, which is the ratio of the rise (the change in y) to the run (the change in x) along the line. The 'b' represents the y-intercept, which is the point where the line crosses the y-axis, and it's the value of y when x is zero.
For example, if we have a line with a slope of 3 and a y-intercept of 9, as described in Figure A1, the equation would be written as y = 3x + 9. This translates to a rise of 3 units in the y-direction for every one unit increase in the x-direction. The line will cross the y-axis at the point (0, 9).
This slope-intercept form is extremely useful as it gives you a quick way to graph the line by starting at the y-intercept and using the slope to find other points on the line. Remember, the slope is constant for a straight line, which means that the proportional change between y and x will stay the same no matter where you are on the line.