How do you graph #3x+4y=-10# using intercepts?

Question

Hazel Anglin · Accepted Answer

See a solution process below:

First, we will find the #x# intercept by solve the equation for #y = #: #3x + (4 * 0) = -10# #3x + 0 = -10# #3x = -10# #(3x)//color(red)(3) = -10/color(red)(3)# #x = -10/3# or #(-10/3, 0)# Next, we will find the #y# intercept by solve the equation for #x = #: #(3 xx 0) + 4y = -10# #0 + 4y = -10# #4y = -10# #(4y)//color(red)(4) = -10/color(red)(4)# #y = -5/2# or #(0, -5/2)# We can then plot the two intercepts on the coordinate plane: graph{(x^2+(y+(5/2))^2-0.025)((x+(10/3))^2+y^2-0.025)=0 [-10, 10, -5, 5]} Now, we can draw a straight line through the two points to graph the line: graph{(3x + 4y + 10)(x^2+(y+(5/2))^2-0.025)((x+(10/3))^2+y^2-0.025)=0 [-10, 10, -5, 5]}

Genesis Allen · Answer

undefined To graph the equation 3x + 4y = -10 using intercepts, first find the x-intercept by setting y = 0 and solving for x: 3x + 4(0) = -10. This simplifies to 3x = -10, so x = -10/3. Then find the y-intercept by setting x = 0 and solving for y: 3(0) + 4y = -10. This simplifies to 4y = -10, so y = -10/4 or -5/2. Plot these points (-10/3, 0) and (0, -5/2) on the coordinate plane, and draw a line through them to represent the graph of the equation.