Which of the following points lie on a line that passes through the origin with a slope of −25? Select all that apply
To determine which points lie on the line passing through the origin with a slope of -25, we can use the equation of a line, which is given by the formula y = mx, where m represents the slope.
Given that the slope is -25, the equation of the line becomes y = -25x.
Now let's plug in the values for x and y from the given options and check if they satisfy the equation:
1) (0,0): When x = 0, the equation becomes y = -25(0) = 0. This point satisfies the equation since y = 0, and indeed lies on the line passing through the origin with a slope of -25.
2) (1, -25): When x = 1, the equation becomes y = -25(1) = -25. This point satisfies the equation since y = -25, and indeed lies on the line passing through the origin with a slope of -25.
3) (-5, 125): When x = -5, the equation becomes y = -25(-5) = 125. This point satisfies the equation since y = 125, and indeed lies on the line passing through the origin with a slope of -25.
Therefore, all of the given options (0,0), (1, -25), and (-5, 125) lie on a line that passes through the origin with a slope of -25.