Final answer:
To find the x-value of the x-intercept for the line containing points (-9,-7) and (13,-19), calculate the equation of the line and solve for x when y=0. The x-intercept x-value is approximately 3.17.
Step-by-step explanation:
To find the x-value of the x-intercept of a line containing the points (-9,-7) and (13,-19), one would first need to determine the equation of the line in the slope-intercept form, which is y=mx+b. The slope (m) can be calculated using the formula m=(y2-y1)/(x2-x1).
For the points (-9,-7) and (13,-19), the slope m will be (−19 - (−7))/(13 - (−9)) = (-12)/(22) = -6/11. Once we have the slope, we use one of the points to find the y-intercept (b) using the equation y=mx+b. Let's use (-9,-7): -7 = (-6/11)(-9) + b. Solving this for b gives us b=-19/11.
Now we have the equation y=(-6/11)x - 19/11. To find the x-intercept, we set y to 0 and solve for x: 0 = (-6/11)x - 19/11; which gives us x = 19/6. This evaluates to approximately 3.17 when rounded to two decimal places.