The graph of a linear equation contains the points (3, 11), and (-2, 1). Which points also lies on the graph?

Question

Eva Adamson · Accepted Answer

Any point on the graph #y=2x+5#
For example, (2,9) or (1,7)

The graph of a linear equation usually takes place in the form of #y=mx+b#, where #m# is the gradient, #b# is the #y#-intercept, #y# is the dependent value, and #x# is the independent value. To write a linear equation given two points of #(x_1,y_1)# and #(x_2,y_2)#, we use the formula #(y_1-y_2)/(x_1-x_2)=m#, where #m# is the gradient. Since we have the two points of (3,11) and (-2,1), we substitute them into the formula to get #(11-1)/(3--2)=m# #10/5=m# #2=m# So far our linear equation looks like this: #y=2x+b# We now have to find #b#, and to do that we substitute in one of our known points (3,11) into the equation, like so: #11=2*3 + b# #11=6+b# #5=b# Since #b=5#, we now have our equation of #y=2x+5#, which when graphed looks like this: graph{y=2x+5 [-10, 10, -5.21, 5.21]} To find other points on this graph simply locate them on the line, or complete the linear equation using different value of #x# and #y#. I hope I helped!

Savannah Anderson · Answer

undefined To find other points on the graph of the linear equation, calculate the equation's slope using the given points. Then, use the slope to find additional points on the graph.