Consider a slide shaped like a right triangle. The base of the slide is 45 feet away from the ladder. The top of the slide is 20 feet high. a) What is the slope of the slide. b) write an equation for the line that the slide would form. c) Lets say you were standing at the bottom of the slide and walked 27 feet closer to the ladder. How high is the slide at this point? d)If the slide was 50 feet long, what would be the new slope
a) To find the slope of the slide, we can use the formula: slope = (change in vertical distance) / (change in horizontal distance). In this case, the change in vertical distance is 20 feet (from the base to the top) and the change in horizontal distance is 45 feet (from the base to the ladder). So, the slope of the slide is 20/45 = 4/9.
b) To write an equation for the line that the slide would form, we can use the slope-intercept form of a line equation: y = mx + b, where m is the slope and b is the y-intercept. The slope of the slide is 4/9. Since the slide starts at a height of 20 feet when the base is 45 feet away from the ladder, the y-intercept is 20. Therefore, the equation for the line that the slide would form is y = (4/9)x + 20.
c) If you were standing at the bottom of the slide and walked 27 feet closer to the ladder, the new horizontal distance would be 45 - 27 = 18 feet. We can use the equation from part b to find the new height of the slide. Plugging in x = 18 into the equation y = (4/9)x + 20, we get y = (4/9) * 18 + 20 = 8 + 20 = 28 feet. So, the slide would be 28 feet high at this point.
d) If the slide was 50 feet long, the new horizontal distance would be 50 feet. We can use the equation from part b to find the new slope. Plugging in x = 50 into the equation y = (4/9)x + 20, we get y = (4/9) * 50 + 20 = 22.22 + 20 = 42.22 feet. So, the new slope would be 42.22 feet.