QuestionFind the $y$ -intercept and slope of the line given by $4 x + 2 y = -2$ . Provide answers in simplest form.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given in the form $ax + by = c$ . . The $y$ -intercept is the point where the line crosses the $y$ -axis, i.e., when $x =0$ .
3. The slope of a line in the form $ax + by = c$ is $-a/b$ .

STEP 2

First, let's find the $y$ -intercept. We can do this by setting $x =0$ in the equation and solving for $y$ .
$4(0) +2y = -2$

STEP 3

implify the equation to find the $y$ -intercept.
$2y = -2$

STEP 4

olve for $y$ to find the $y$ -intercept.
$y = -2 /2$

STEP 5

Calculate the $y$ -intercept.
$y = -2 /2 = -1$ So, the $y$ -intercept is $-1$ .

STEP 6

Now, let's find the slope of the line. The slope of a line in the form $ax + by = c$ is $-a/b$ . In this case, $a =4$ and $b =2$ .
$lope = -a/b$

STEP 7

Substitute the values of $a$ and $b$ into the formula to find the slope.
$lope = -4/2$

STEP 8

Calculate the slope.
$lope = -4/2 = -2$ So, the slope of the line is $-2$ .

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QuestionFind the $y$ -intercept and slope of the line given by $4 x + 2 y = -2$ . Provide answers in simplest form.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given in the form $ax + by = c$ . . The $y$ -intercept is the point where the line crosses the $y$ -axis, i.e., when $x =0$ .
3. The slope of a line in the form $ax + by = c$ is $-a/b$ .

STEP 2

First, let's find the $y$ -intercept. We can do this by setting $x =0$ in the equation and solving for $y$ .
$4(0) +2y = -2$

STEP 3

implify the equation to find the $y$ -intercept.
$2y = -2$

STEP 4

olve for $y$ to find the $y$ -intercept.
$y = -2 /2$

STEP 5

Calculate the $y$ -intercept.
$y = -2 /2 = -1$ So, the $y$ -intercept is $-1$ .

STEP 6

Now, let's find the slope of the line. The slope of a line in the form $ax + by = c$ is $-a/b$ . In this case, $a =4$ and $b =2$ .
$lope = -a/b$

STEP 7

Substitute the values of $a$ and $b$ into the formula to find the slope.
$lope = -4/2$

STEP 8

Calculate the slope.
$lope = -4/2 = -2$ So, the slope of the line is $-2$ .

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QuestionFind the yyy-intercept and slope of the line given by 4x+2y=−24 x + 2 y = -24x+2y=−2. Provide answers in simplest form.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given in the form ax+by=cax + by = cax+by=c. . The yyy-intercept is the point where the line crosses the yyy-axis, i.e., when x=0x =0x=0.3. The slope of a line in the form ax+by=cax + by = cax+by=c is −a/b-a/b−a/b.

STEP 2

First, let's find the yyy-intercept. We can do this by setting x=0x =0x=0 in the equation and solving for yyy.4(0)+2y=−24(0) +2y = -24(0)+2y=−2

STEP 3

implify the equation to find the yyy-intercept.2y=−22y = -22y=−2

STEP 4

olve for yyy to find the yyy-intercept.y=−2/2y = -2 /2y=−2/2

STEP 5

Calculate the yyy-intercept.y=−2/2=−1y = -2 /2 = -1y=−2/2=−1So, the yyy-intercept is −1-1−1.

STEP 6

Now, let's find the slope of the line. The slope of a line in the form ax+by=cax + by = cax+by=c is −a/b-a/b−a/b. In this case, a=4a =4a=4 and b=2b =2b=2.lope=−a/blope = -a/blope=−a/b

STEP 7

Substitute the values of aaa and bbb into the formula to find the slope.lope=−4/2lope = -4/2lope=−4/2

STEP 8

Calculate the slope.lope=−4/2=−2lope = -4/2 = -2lope=−4/2=−2So, the slope of the line is −2-2−2.

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QuestionFind the $y$ -intercept and slope of the line given by $4 x + 2 y = -2$ . Provide answers in simplest form.

Assumptions1. The equation of the line is given in the form $ax + by = c$ . . The $y$ -intercept is the point where the line crosses the $y$ -axis, i.e., when $x =0$ .
3. The slope of a line in the form $ax + by = c$ is $-a/b$ .

First, let's find the $y$ -intercept. We can do this by setting $x =0$ in the equation and solving for $y$ .
$4(0) +2y = -2$

implify the equation to find the $y$ -intercept.
$2y = -2$

olve for $y$ to find the $y$ -intercept.
$y = -2 /2$

Calculate the $y$ -intercept.
$y = -2 /2 = -1$ So, the $y$ -intercept is $-1$ .

Now, let's find the slope of the line. The slope of a line in the form $ax + by = c$ is $-a/b$ . In this case, $a =4$ and $b =2$ .
$lope = -a/b$

Substitute the values of $a$ and $b$ into the formula to find the slope.
$lope = -4/2$

Calculate the slope.
$lope = -4/2 = -2$ So, the slope of the line is $-2$ .