How do you graph the equation by plotting points #y = x - 2#?

Question

Eva Adamson · Accepted Answer

See below

This is the equation of a line, so you only need two points to plot it. To find two points on the line, plug two random #x# values and compute the corresponding #y# values. For example, let's choose #x=0# and #x=1#. #x = 0# yields #y = 0 - 2 = -2# So, the first point is #(0,-2)# #x = 1# yields #y = 1 - 2 = -1# So, the first point is #(1,-1)# Draw the two points and connect them, and you have the line

Eva Adamson · Answer

#"see explanation"# #"one way is to find the intercepts, that is where the graph"# #"crosses the x and y axes"# #• " let x = 0, in the equation for y-intercept"# #• " let y = 0, in the equation for x-intercept"# #x=0rArry=-2larrcolor(red)"y-intercept"# #y=0rArrx-2=0rArrx=2larrcolor(red)"x-intercept"# #"plot the points "(0,-2)" and "(2,0)# #"draw a straight line through them for graph"# graph{(y-x+2)((x-0)^2+(y+2)^2-0.04)((x-2)^2+(y-0)^2-0.04)=0 [-10, 10, -5, 5]}

Avery Alexander · Answer

undefined To graph the equation $ y = x - 2 $ by plotting points:

1. Choose a range of values for $ x $, such as -3, -2, -1, 0, 1, 2, 3, etc.
2. Substitute each $ x $ value into the equation to find the corresponding $ y $ value.
3. Plot each pair of coordinates $(x, y)$ on a Cartesian plane.
4. Connect the plotted points with a straight line.

Here are some sample points and their corresponding coordinates:

For $ x = -3 $, $ y = -3 - 2 = -5 $, so the point is $(-3, -5)$.
For $ x = -2 $, $ y = -2 - 2 = -4 $, so the point is $(-2, -4)$.
For $ x = -1 $, $ y = -1 - 2 = -3 $, so the point is $(-1, -3)$.
For $ x = 0 $, $ y = 0 - 2 = -2 $, so the point is $(0, -2)$.
For $ x = 1 $, $ y = 1 - 2 = -1 $, so the point is $(1, -1)$.
For $ x = 2 $, $ y = 2 - 2 = 0 $, so the point is $(2, 0)$.
For $ x = 3 $, $ y = 3 - 2 = 1 $, so the point is $(3, 1)$.

Plotting these points and connecting them with a straight line will give you the graph of the equation $ y = x - 2 $.