How do you graph #y=-5x+10# using intercepts?

Question

Nathan Axel · Accepted Answer

See a solution process below:

First, find the #y#-intercept by setting #x# to #0# and calculating #y#: y-intercept: #y = (-5 * 0) + 10# #y = 0 + 10# #y = 10# or #(0, 10)# Next, find the #x#-intercept by setting #y# to #0# and solving for #x#: x-intercept: #0 = -5x + 10# #0 - color(red)(10) = -5x + 10 - color(red)(10)# #-10 = -5x + 0# #-10 = -5x# #(-10)/color(red)(-5) = (-5x)/color(red)(-5)# #2 = (color(red)(cancel(color(black)(-5)))x)/cancel(color(red)(-5))# #2 = x# #x = 2# or #(2, 0)# We can next graph the two points on the coordinate plane: graph{(x^2+(y-10)^2-0.125)((x-2)^2+y^2-0.125)=0 [-25, 25, -12.5, 12.5]} Now, we can draw a straight line through the two points to graph the line: graph{(y+5x-10)(x^2+(y-10)^2-0.125)((x-2)^2+y^2-0.125)=0 [-25, 25, -12.5, 12.5]}

Jace Anderson · Answer

undefined To graph the equation $y = -5x + 10$ using intercepts:
1. Find the x-intercept by setting $y = 0$ and solving for $x$:  
   $0 = -5x + 10$  
   $5x = 10$  
   $x = 2$  
   So, the x-intercept is (2, 0).
   
2. Find the y-intercept by setting $x = 0$ and solving for $y$:  
   $y = -5(0) + 10$  
   $y = 10$  
   So, the y-intercept is (0, 10).

Plot the x-intercept at (2, 0) and the y-intercept at (0, 10), then draw a straight line passing through these two points to graph the equation $y = -5x + 10$.