OG详解-OG4 数学1 Q12

Choice C is correct. An equation of a line can be written in the form y = mx + b, where m is the slope of the line and (0, b) is the y-intercept of the line. The line shown passes through the point (0, -8), so b =-8. The line shown also passes through the point (-8, 0). The slope, m, of a line passing through two points (x₁, ​y₁)  and (x₂, ​y₂) can be calculated using the equation m = y₂−y₁x₂−x_1​​ . For the points (0, -8) and (-8, 0), this gives m =  (−8)−00−(−8​)​, or m =-1. Substituting -8 for b and -1 for m in y = mx + b yields y =(-1)x +(-8), or y =-x -8. Therefore, an equation of the graph shown is y =-x-8.
Choice A is incorrect. This is an equation of a line with a slope of -2, not -1. Choice B is incorrect. This is an equation of a line with a slope of 1, not -1. Choice D is incorrect. This is an equation of a line with a slope of 2, not -1.