Final answer:
The equation of the line containing points (9, 3) and (19, -17) is found by first calculating the slope, which is -2. Then, using one of the points, the y-intercept is determined to be 21. Therefore, the equation in slope-intercept form is y = -2x + 21.
Step-by-step explanation:
To find the equation of a line in slope-intercept form that contains the points (9, 3) and (19, -17), we first calculate the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting in our points gives us:
m = (-17 - 3) / (19 - 9) = -20 / 10 = -2
Now that we have the slope, we can use one of the points and the slope to solve for the y-intercept (b), using the slope-intercept form equation, y = mx + b.
Let's use the point (9, 3). Plugging the values into the equation:
3 = (-2)(9) + b
3 = -18 + b
b = 3 + 18
b = 21
The equation of the line is thus: y = -2x + 21
This line has a slope of -2, indicating a fall of 2 on the vertical axis for every increase of 1 on the horizontal axis, and it intersects the y-axis at 21. This is how the slope and y-intercept determine the shape of the line.