How do you graph using the intercepts for #2x + 3y = 8#?

1 Answer
Jun 11, 2018

Answer:

The #x# intercept is the point #(4,0)#

The #y# intercept is the point #(0,8/3)#

Connect the two points to draw the line

Explanation:

To look for intercepts means to look for points where a given graph meets one of the axis.

The #x# axis is the set of all points with coordinates like #(x,0)#, i.e. their #y# coordinate is zero.

Similarly, the #y# axis is the set of all points with coordinates like #(0,y)#, i.e. their #x# coordinate is zero.

So, if we want to find the #x# intercept, we need to set #y=0# and solve for #x#: the equation becomes

#2x+3*0=8 \implies 2x = 8 \implies x=4#

So, the #x# intercept is the point #(4,0)#

Similarly, to find the #y# intercept we set #x=0# and solve for #y#:

#2*0+3y=8 \implies 3y=8 \implies y=8/3#

So, the #y# intercept is the point #(0,8/3)#

Since the equation we're working on represents a line, it is sufficient to connect the two points we've just found to draw the graph.