Final answer:
To find the value of x for the given points, we can use the slope-intercept form of a linear equation and substitute the coordinates of one of the points. The equation of the line is y = -1/5x + 4. Plugging in the x-coordinate of the second point, we find that x = 12/5.
Step-by-step explanation:
To find the value of x so that the points (-2, 5) and (8, x) lie on the line with a slope of -1/5, we can use the slope-intercept form of a linear equation, which is y = mx + b. We know that the slope of the line is -1/5, so the equation becomes y = -1/5x + b. To find the y-intercept (b), we can substitute the coordinates of one of the points into the equation. Taking the point (-2, 5), we have 5 = -1/5(-2) + b. Simplifying this equation gives us b = 4. Therefore, the equation of the line is y = -1/5x + 4.
To find the value of x for the point (8, x), we can substitute the x-coordinate (8) into the equation and solve for x. Plugging in x = 8, we have y = -1/5(8) + 4. Simplifying this equation gives us y = -8/5 + 4, which gives y = -8/5 + 20/5, or y = 12/5. Therefore, the value of x that makes the point (8, x) lie on the line is x = 12/5.