Final answer:
To graph a line, plot the y-intercept on the y-axis and use the slope to determine the direction and steepness. Plot another point using the slope and draw a straight line through both points.
Step-by-step explanation:
To graph a line using its slope and y-intercept, you start by plotting the y-intercept on the vertical axis. In Figure A1, the y-intercept is 9, which means the line will intersect the y-axis at the point (0,9). Place a point on the y-axis at that position.
Next, use the slope to determine the direction and steepness of the line. In our example, the slope is 3, which means for every 1 unit increase in x (horizontal axis), the value of y (vertical axis) increases by 3 units. This "rise over run" can be plotted by starting from the y-intercept (0,9), moving one unit to the right (which is the run), and then moving three units up (which is the rise).
After marking a second point using the slope, draw a straight line through these two points. This line represents the equation of the straight line. Remember that in the slope-intercept form of a linear equation, y = a + bx, 'b' represents the slope and 'a' represents the y-intercept, which can be seen at the point (0, a), where the line crosses the y-axis.