QuestionFind the intercepts of the equation $-x + 3y = -3$ . What are the $x$ and $y$ intercepts?

Studdy Solution

STEP 1

Assumptions1. The equation of the line is $-x+3y=-3$ . To find the x-intercept, we set $y=0$ and solve for $x$
3. To find the y-intercept, we set $x=0$ and solve for $y$

STEP 2

To find the x-intercept, we set $y=0$ in the equation and solve for $x$ .
$-x+(0)=-$

STEP 3

implify the equation and solve for $x$ .
$-x=-3$

STEP 4

Multiply both sides of the equation by $-1$ to isolate $x$ .
$x=3$ So, the x-intercept is $(3,0)$ .

STEP 5

To find the y-intercept, we set $x=0$ in the equation and solve for $y$ .
$-(0)+3y=-3$

STEP 6

implify the equation and solve for $y$ .
$3y=-3$

STEP 7

Divide both sides of the equation by $3$ to isolate $y$ .
$y=-1$ So, the y-intercept is $(0,-1)$ .
The intercepts of the line $-x+3y=-3$ are $(3,0)$ and $(0,-1)$ .

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QuestionFind the intercepts of the equation $-x + 3y = -3$ . What are the $x$ and $y$ intercepts?

Studdy Solution

STEP 1

Assumptions1. The equation of the line is $-x+3y=-3$ . To find the x-intercept, we set $y=0$ and solve for $x$
3. To find the y-intercept, we set $x=0$ and solve for $y$

STEP 2

To find the x-intercept, we set $y=0$ in the equation and solve for $x$ .
$-x+(0)=-$

STEP 3

implify the equation and solve for $x$ .
$-x=-3$

STEP 4

Multiply both sides of the equation by $-1$ to isolate $x$ .
$x=3$ So, the x-intercept is $(3,0)$ .

STEP 5

To find the y-intercept, we set $x=0$ in the equation and solve for $y$ .
$-(0)+3y=-3$

STEP 6

implify the equation and solve for $y$ .
$3y=-3$

STEP 7

Divide both sides of the equation by $3$ to isolate $y$ .
$y=-1$ So, the y-intercept is $(0,-1)$ .
The intercepts of the line $-x+3y=-3$ are $(3,0)$ and $(0,-1)$ .

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QuestionFind the intercepts of the equation −x+3y=−3-x + 3y = -3−x+3y=−3. What are the xxx and yyy intercepts?

Studdy Solution

STEP 1

Assumptions1. The equation of the line is −x+3y=−3-x+3y=-3−x+3y=−3 . To find the x-intercept, we set y=0y=0y=0 and solve for xxx3. To find the y-intercept, we set x=0x=0x=0 and solve for yyy

STEP 2

To find the x-intercept, we set y=0y=0y=0 in the equation and solve for xxx.−x+(0)=−-x+(0)=-−x+(0)=−

STEP 3

implify the equation and solve for xxx.−x=−3-x=-3−x=−3

STEP 4

Multiply both sides of the equation by −1-1−1 to isolate xxx.x=3x=3x=3So, the x-intercept is (3,0)(3,0)(3,0).

STEP 5

To find the y-intercept, we set x=0x=0x=0 in the equation and solve for yyy.−(0)+3y=−3-(0)+3y=-3−(0)+3y=−3

STEP 6

implify the equation and solve for yyy.3y=−33y=-33y=−3

STEP 7

Divide both sides of the equation by 333 to isolate yyy.y=−1y=-1y=−1So, the y-intercept is (0,−1)(0,-1)(0,−1).The intercepts of the line −x+3y=−3-x+3y=-3−x+3y=−3 are (3,0)(3,0)(3,0) and (0,−1)(0,-1)(0,−1).

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QuestionFind the intercepts of the equation $-x + 3y = -3$ . What are the $x$ and $y$ intercepts?

Assumptions1. The equation of the line is $-x+3y=-3$ . To find the x-intercept, we set $y=0$ and solve for $x$
3. To find the y-intercept, we set $x=0$ and solve for $y$

To find the x-intercept, we set $y=0$ in the equation and solve for $x$ .
$-x+(0)=-$

implify the equation and solve for $x$ .
$-x=-3$

Multiply both sides of the equation by $-1$ to isolate $x$ .
$x=3$ So, the x-intercept is $(3,0)$ .

To find the y-intercept, we set $x=0$ in the equation and solve for $y$ .
$-(0)+3y=-3$

implify the equation and solve for $y$ .
$3y=-3$

Divide both sides of the equation by $3$ to isolate $y$ .
$y=-1$ So, the y-intercept is $(0,-1)$ .
The intercepts of the line $-x+3y=-3$ are $(3,0)$ and $(0,-1)$ .