Final answer:
To find the equation of the line through the origin and (-5, 6), the slope is calculated as -6/5. Since the line passes through the origin, its y-intercept is 0. Therefore, the equation is y = -6x/5 or y = -1.2x, which is not listed in the given choices.
Step-by-step explanation:
To find the equation of the line passing through the origin and the point (-5, 6), we will first calculate the slope of the line. The slope (m) is the rise over the run, which in this case is the change in y divided by the change in x. Using the two points (0,0) and (-5,6), the slope can be calculated as follows:
m = (6 - 0) / (-5 - 0) = 6 / -5 = -6/5
Since the line passes through the origin, its y-intercept (b) is 0. Therefore, the equation of the line in slope-intercept form (y = mx + b) is:
y = (-6/5)x + 0
To match one of the answer choices provided, we can multiply both numerator and denominator by 5 to simplify:
y = -6x/5 or y = -1.2x, which is not explicitly listed among the choices given. Hence, none of the provided answer choices A, B, C or D are correct.