How do you graph #y= -2x#?

Question

Genesis Allen · Accepted Answer

Refer to the explanation.

Graph: #y=-2x# is a linear equation in slope-intercept form: #y=mx+b,# where: #m# is the slope and #b# is the y-intercept. Determine the x- and y-intercepts. The x-intercept is the value of #x# when #y=0#, and the y-intercept is the value of #y# when #x=0#. According to the slope-intercept equation, the y-intercept in the given equation is #0#, and the point is #(0,0)#. To determine the x-intercept, substitute #0# for #y# and solve for #x#. #0=-2x# Divide both sides by #-2#. #0/(-2)=x# #0=x# The x-intercept is #0# and the point is #(0,0)#. The line will go through the origin. Plot the x- and y-intercepts and draw a straight line through them. graph{y=-2x [-10, 10, -5, 5]}

Julia Adams · Answer

undefined To graph the equation $ y = -2x $, you need to plot points on a coordinate plane. Since it's a linear equation in slope-intercept form ($ y = mx + b $), where $ m $ represents the slope and $ b $ represents the y-intercept, in this case, the slope ($ m $) is -2 and there is no y-intercept.

To plot the graph:
1. Choose several values for $ x $.
2. Plug each $ x $ value into the equation to find the corresponding $ y $ value.
3. Plot each point ($ x, y $) on the coordinate plane.
4. Draw a straight line passing through these points.

For example:
- When $ x = 0 $, $ y = -2(0) = 0 $. So, the point (0, 0) is on the line.
- When $ x = 1 $, $ y = -2(1) = -2 $. So, the point (1, -2) is on the line.
- When $ x = -1 $, $ y = -2(-1) = 2 $. So, the point (-1, 2) is on the line.

Plotting these points and drawing a straight line passing through them will give you the graph of $ y = -2x $.