Question

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

Answer 1

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.