The x-intercept of a line is found where y=0. By considering the slope of the given points and using the slope-intercept form of the equation, y=mx+b, the x-intercept is calculated to be (22, 0).
To find the x-intercept of a line, you need to determine where the line crosses the x-axis. This occurs where the y-value is equal to 0.
Considering the given points (-38, 40), (-23, 30), and (-8, 20), we can observe that the y-value decreases by 10 whenever the x-value increases by 15.
This suggests a consistent slope. By setting up the equation of the line using the slope-intercept form, y = mx + b, we can calculate the slope (m) and use one of the points to find the y-intercept (b). In this case:
m = change in y / change in x = (30 - 40) / (-23 + 38) = -10 / 15 = -2/3
Using the point (-38, 40), we can plug the values into the slope-intercept form to find b:
40 = (-2/3)(-38) + b
b = 40 - 76/3
b = 40 - 25.333...
b = 14.666...
The equation of the line is then y = (-2/3)x + 14.666...
Now, we set y to 0 to find the x-intercept:
0 = (-2/3)x + 14.666...
x = 14.666... / (2/3)
x = 22
Therefore, the x-intercept is (22, 0).