Find the x- and y-intercepts for the equation. Then graph the equation.
-$6 y-2 x=-10$

A) $\left( 0 , - \frac { 5 } { 3 } \right) , ( 5,0 )$
B) $\left( 0 , - \frac { 5 } { 3 } \right) , ( - 5,0 )$

Question

Find the x- and y-intercepts for the equation. Then graph the equation.
-$6 y-2 x=-10$

A) $\left( 0 , - \frac { 5 } { 3 } \right) , ( 5,0 )$ 
B) $\left( 0 , - \frac { 5 } { 3 } \right) , ( - 5,0 )$

Quizplus · Accepted Answer

To find the x-intercept, we let y = 0 and solve for x:

\begin{align*}
6y-2x&=-10 \
6(0)-2x&=-10 \
-2x &= -10 \
x &= 5 \
\end{align*}

Therefore, the x-intercept is (5,0).

To find the y-intercept, we let x = 0 and solve for y:

\begin{align*}
6y-2x&=-10 \
6y-2(0)&=-10 \
6y &= -10 \
y &= -\frac{5}{3} \
\end{align*}

Therefore, the y-intercept is (0,-5/3).

Finally, to graph the equation, we can plot the x- and y-intercepts and draw a straight line passing through them.

[asy]
size(150);
import TrigMacros;

void axes(real x0, real x1, real y0, real y1)
{
	draw((x0,0)--(x1,0),EndArrow);
    draw((0,y0)--(0,y1),EndArrow);
    label("$x$",(x1,0),(2,0));
    label("$y$",(0,y1),(0,2));
    for (int i=floor(x0)+1; i<x1; ++i)
    	draw((i,.1)--(i,-.1));
    for (int i=floor(y0)+1; i<y1; ++i)
    	draw((.1,i)--(-.1,i));
}

axes(-6,6,-3,3);
draw((-6,5/3)--(6,-20/3),Arrows);
dot((0,-5/3),red);
dot((5,0),red);
[/asy]

Find the X- and Y-Intercepts for the Equation 6y−2x=−106 y-2 x=-106y−2x=−10

Find the X- and Y-Intercepts for the Equation $6 y-2 x=-10$