To prove that the line y = -5x + 10 passes through the point (3,-5) and is perpendicular to the line y = 1/5x - 2, we need to show two things:
1. The point (3,-5) lies on the line y = -5x + 10.
2. The slope of the line y = -5x + 10 is -5, which is the negative reciprocal of the slope of the line y = 1/5x - 2.
1. To show that the point (3,-5) lies on the line y = -5x + 10, we can substitute x = 3 and y = -5 into the equation y = -5x + 10:
-5 = -5(3) + 10
-5 = -15 + 10
-5 = -5
Since the equation is true, the point (3,-5) lies on the line y = -5x + 10.
2. To show that the slope of the line y = -5x + 10 is -5, we can rewrite the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:
y = -5x + 10
Comparing this to the general form of the slope-intercept equation, we see that the slope is -5. Therefore, the slope of the line y = -5x + 10 is -5.
Since we have shown that the point (3,-5) lies on the line y = -5x + 10 and the slope of the line is -5, which is the negative reciprocal of the slope of the line y = 1/5x - 2, we have proven that the line y = -5x + 10 passes through the point (3,-5) and is perpendicular to the line y = 1/5x - 2.