Question

What is the y intercept of \[3x - 2y = - 6\].

Answer 1

Hint: Recollect the intercept formula. Express the given equation into intercept form and compare.
The intercept formula is given by \[\dfrac{x}{a} + \dfrac{y}{b} = 1\]

Complete step by step answer:
Let \[\left( {a,{\text{ }}b} \right)\] are the \[x\] intercept and $y$ intercepts respectively,
Then the intercept formula is given by \[\dfrac{x}{a} + \dfrac{y}{b} = 1\]
Given equation is \[3x - 2y = - 6\]
 We need to express it in the form of intercept form.
Observe, RHS of the formula, it should be $1$.
Now look at the given equation, RHS is \[ - 6\] so divide the given equation by \[ - 6\] on both sides.
\[\dfrac{{3x}}{{ - 6}} - \dfrac{{2y}}{{ - 6}} = \dfrac{{ - 6}}{{ - 6}}\]
Cancel the terms wherever possible.
\[\dfrac{x}{{ - 2}} + \dfrac{y}{3} = 1\]
Now you compare with the original intercept formula \[\dfrac{x}{a} + \dfrac{y}{b} = 1\]
\[x\]–intercept is \[a{\text{ }} = {\text{ }} - 2\]
$y$-intercept is \[b{\text{ }} = {\text{ }}3\]

Additional information:
The \[x\] intercept is the point where the line crosses the \[x\] axis. The$y$intercept is the point where the line crosses the $y$ axis. At this point\[x{\text{ }} = {\text{ }}0\].The point where the line or curve crosses the axis of the graph is called intercept. If a point crosses the \[x\]-axis, then it is called \[x\]-intercept. If a point crosses the $y$-axis, then it is called $y$-intercept.
The meaning of intercept of a line is the point at which it intersects either the \[x\]-axis or $y$-axis. If the axis is not specified, usually the $y$-axis is considered. It is normally denoted by the letter ‘$b$ ’.
Except that line is accurately vertical, it will constantly cross the $y$-axis somewhere, even if it is way off the top or bottom of the chart.
Have a clear understanding of the terms intercepts along with figures. You can show this with the figures also so that you can attract the examiner to get more marks.

Note: When you are converting it to intercept form please check the RHS and divide with the same on both sides.
Don’t divide only RHS which changes the equation.
When you are cancelling the terms always it is not mandatory that it should be a natural number it may be a fraction also.