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

Feb 20, 2016

$\textcolor{b l u e}{{y}_{\text{intercept") = 3)" "color(blue)(x_("intercept}} = - 1.5}$

Mark these points on the axis and draw a straight line through them.

Explanation:

Given:$\text{ } \textcolor{b r o w n}{- 2 x + y = 3}$

Change this into the standard format of $y = m x + c$

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

color(brown)(color(blue)(2x)-2x+y" "=" "3color(blue)(+2x)

$0 + y = 2 x + 3$

$y = 2 x + 3$............................(1)

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$\textcolor{b l u e}{\text{To find the y intercept}}$

If you look at the graph the plotted line crosses the y-axis when $x = 0$

So substitute $\textcolor{g r e e n}{x = 0}$ into equation (1)

So $y = 2 x + 3 \text{ becomes } y = 2 \left(\textcolor{g r e e n}{0}\right) + 3$

that is:$\text{ "y=(2xxcolor(green)(0))+3" " =" } 0 + 3$

So $\textcolor{red}{{y}_{\text{intercept}} = 3}$

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

If you look at the graph the plotted line crosses the x-axis when $y = 0$

So substitute $\textcolor{g r e e n}{y = 0}$ into equation (1)

So $\textcolor{b r o w n}{y = 2 x + 3} \text{ becomes } \textcolor{b r o w n}{\textcolor{g r e e n}{0} = 2 x + 3}$

Subtract $\textcolor{b l u e}{3}$ from both sides

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

$- 3 = 2 x + 0$

$\textcolor{b r o w n}{2 x = - 3}$

Divide both sides by 2 which is the same as $\textcolor{b l u e}{\times \frac{1}{2}}$

color(brown)(color(blue)(1/2xx) 2x=color(blue)(1/2xx)(-3)

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

But $\frac{2}{2} = 1$ giving:

$x = - \frac{3}{2} \to - 1 \frac{1}{2} \to - 1.5$

$\textcolor{red}{{x}_{\text{intercept}} = - 1.5}$