QuestionFind the intercepts of the line $y=-4x+4$ . Provide answers as points $(x, y)$ for both intercepts.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is $y=-4x+4$ . We are looking for the $x$ -intercept and the $y$ -intercept3. The $x$ -intercept is the point where the line crosses the $x$ -axis (i.e., $y=0$ )
4. The $y$ -intercept is the point where the line crosses the $y$ -axis (i.e., $x=0$ )

STEP 2

First, let's find the $x$ -intercept by setting $y=0$ in the equation of the line.
$0=-4x+4$

STEP 3

Now, solve the equation for $x$ .
$-x+=0$

STEP 4

Rearrange the equation to isolate $x$ .
$-4x=4$

STEP 5

Divide both sides by $-4$ to solve for $x$ .
$x=\frac{4}{-4}$

STEP 6

Calculate the value of $x$ .
$x=\frac{4}{-4}=-1$ So, the $x$ -intercept is $(-1,0)$ .

STEP 7

Now, let's find the $y$ -intercept by setting $x=0$ in the equation of the line.
$y=-4(0)+4$

STEP 8

implify the equation to find the value of $y$ .
$y=4$ So, the $y$ -intercept is $(0,4)$ .
The intercepts of the line $y=-4x+4$ are $(-1,0)$ and $(0,4)$ .

Was this helpful?

QuestionFind the intercepts of the line $y=-4x+4$ . Provide answers as points $(x, y)$ for both intercepts.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is $y=-4x+4$ . We are looking for the $x$ -intercept and the $y$ -intercept3. The $x$ -intercept is the point where the line crosses the $x$ -axis (i.e., $y=0$ )
4. The $y$ -intercept is the point where the line crosses the $y$ -axis (i.e., $x=0$ )

STEP 2

First, let's find the $x$ -intercept by setting $y=0$ in the equation of the line.
$0=-4x+4$

STEP 3

Now, solve the equation for $x$ .
$-x+=0$

STEP 4

Rearrange the equation to isolate $x$ .
$-4x=4$

STEP 5

Divide both sides by $-4$ to solve for $x$ .
$x=\frac{4}{-4}$

STEP 6

Calculate the value of $x$ .
$x=\frac{4}{-4}=-1$ So, the $x$ -intercept is $(-1,0)$ .

STEP 7

Now, let's find the $y$ -intercept by setting $x=0$ in the equation of the line.
$y=-4(0)+4$

STEP 8

implify the equation to find the value of $y$ .
$y=4$ So, the $y$ -intercept is $(0,4)$ .
The intercepts of the line $y=-4x+4$ are $(-1,0)$ and $(0,4)$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the intercepts of the line y=−4x+4y=-4x+4y=−4x+4. Provide answers as points (x,y)(x, y)(x,y) for both intercepts.

Studdy Solution

STEP 1

STEP 2

First, let's find the xxx-intercept by setting y=0y=0y=0 in the equation of the line.0=−4x+40=-4x+40=−4x+4

STEP 3

Now, solve the equation for xxx.−x+=0-x+=0−x+=0

STEP 4

Rearrange the equation to isolate xxx.−4x=4-4x=4−4x=4

STEP 5

Divide both sides by −4-4−4 to solve for xxx.x=4−4x=\frac{4}{-4}x=−44​

STEP 6

Calculate the value of xxx.x=4−4=−1x=\frac{4}{-4}=-1x=−44​=−1So, the xxx-intercept is (−1,0)(-1,0)(−1,0).

STEP 7

Now, let's find the yyy-intercept by setting x=0x=0x=0 in the equation of the line.y=−4(0)+4y=-4(0)+4y=−4(0)+4

STEP 8

implify the equation to find the value of yyy.y=4y=4y=4So, the yyy-intercept is (0,4)(0,4)(0,4).The intercepts of the line y=−4x+4y=-4x+4y=−4x+4 are (−1,0)(-1,0)(−1,0) and (0,4)(0,4)(0,4).

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the intercepts of the line $y=-4x+4$ . Provide answers as points $(x, y)$ for both intercepts.

First, let's find the $x$ -intercept by setting $y=0$ in the equation of the line.
$0=-4x+4$

Now, solve the equation for $x$ .
$-x+=0$

Rearrange the equation to isolate $x$ .
$-4x=4$

Divide both sides by $-4$ to solve for $x$ .
$x=\frac{4}{-4}$

Calculate the value of $x$ .
$x=\frac{4}{-4}=-1$ So, the $x$ -intercept is $(-1,0)$ .

Now, let's find the $y$ -intercept by setting $x=0$ in the equation of the line.
$y=-4(0)+4$

implify the equation to find the value of $y$ .
$y=4$ So, the $y$ -intercept is $(0,4)$ .
The intercepts of the line $y=-4x+4$ are $(-1,0)$ and $(0,4)$ .