How do you find the x and y intercepts for  y=3x-2 ?

Jan 22, 2016

$y = - 2$ and $x = \frac{2}{3}$

Explanation:

This is the equation of a straight line. When the line crosses the x-axis the y-coordinate will be zero. By Putting $y = 0$ we can find the corresponding value of x (the x-intercept ).

Put $y = 0$ : $3 x - 2 = 0$ so $3 x = 2$$\Rightarrow x = \frac{2}{3}$

Similarly , when the line crosses the y-axis the x-coordinate will be zero. Put $x = 0$ to find the y-intercept.

Put $x = 0$ : $y = 0 - 2$ $\Rightarrow y = - 2$

Jan 22, 2016

$\textcolor{b l u e}{\text{ y-intercept} \to y = - 2}$
color(blue)(" x-intercept"->x=2/3_

Explanation:

Given:$\textcolor{w h i t e}{\ldots . .} y = 3 x - 2$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{To find the x-intercept}}$

This is a strait line graph so you will find that the plotted line crosses the y-axis (intercept) at the same value as the constant of $- 2$

Why is this?

The y-axis crosses the x-axis at $x = 0$. That means that the plot also crosses (intercept) the y-axis at $x = 0$. So if we substitute $x = 0$ into the equation we get:

$y = \left(3 \times 0\right) - 2$

$\textcolor{b l u e}{\text{y-intercept} \to y = - 2}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{To find the x-intercept}}$

By the same logic, the plotted line crosses (intercept) the x-axis at y=0. So if we substitute $y = 0$ into the equation then we have:

$y = 3 x - 2 \textcolor{w h i t e}{. x . .} \to \textcolor{w h i t e}{. x . .} \textcolor{b r o w n}{0 = 3 x - 2}$

Add $\textcolor{b l u e}{2}$ to both sides:

$\textcolor{b r o w n}{0 \textcolor{b l u e}{+ 2} = 3 x - 2 \textcolor{b l u e}{+ 2}}$

$\textcolor{g r e e n}{2 = 3 x + 0}$

Divide both sides by $\textcolor{b l u e}{3}$

color(green)(2/(color(blue)(3))=(3x)/(color(blue)(3))

$\frac{2}{3} = \frac{3}{3} \times x$

But 3/3 = 1 giving:

$\frac{2}{3} = x$

color(blue)("x-intercept"->x=2/3_
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~