Question

How do you find the x and y intercepts of `14-3x=7y`?

Answer 1

x-intercept: `-14/3color(white)("XXX")`y-intercept: `2`

Explanation:

For all points on the Y-axis, `x=0`
The y-intercept is the value of `y` where the graph of the relation crosses the Y-axis.
Stated another way, the y-intercept is the value of `y` given by the relationship when `x=0`
If `color(red)x=color(red)0`
then `14-3color(red)x=7y`
`rarr 14=7y`
`rarr y=2`
So the y-intercept is `2` (that is the point `(x,y)=(0,2)`)

Similarly the x-intercept is the value of `x` given by the relationship when `y=0`
If `color(blue)y=color(blue)0`
then `14-3x=7color(blue)y`
`rarr 14-3x=0`
`rarr x=-14/3`
So the x-intercept is `-14/3` (that is the point `(x,y)=(-14/3,0)`)