QuestionFind the intercepts of the line given by $-4x + 7y = 3$ . Provide exact values.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given by $-4x +7y =3$ . . The $x$ -intercept of a line is the point where the line crosses the $x$ -axis. At this point, $y =0$ .
3. The $y$ -intercept of a line is the point where the line crosses the $y$ -axis. At this point, $x =0$ .

STEP 2

To find the $x$ -intercept, we set $y =0$ in the equation of the line and solve for $x$ .
$-4x +7(0) =$

STEP 3

implify the equation to find the $x$ -intercept.
$-x =3$

STEP 4

To isolate $x$ , divide both sides of the equation by $-4$ .
$x = \frac{3}{-4}$

STEP 5

Calculate the $x$ -intercept.
$x = -\frac{3}{4}$ So, the $x$ -intercept is $(-\frac{3}{4},0)$ .

STEP 6

To find the $y$ -intercept, we set $x =0$ in the equation of the line and solve for $y$ .
$-4(0) +y =3$

STEP 7

implify the equation to find the $y$ -intercept.
$7y =3$

STEP 8

To isolate $y$ , divide both sides of the equation by $7$ .
$y = \frac{3}{7}$

STEP 9

Calculate the $y$ -intercept.
$y = \frac{3}{7}$ So, the $y$ -intercept is $(, \frac{3}{7})$ .
The $x$ -intercept is $(-\frac{3}{4},)$ and the $y$ -intercept is $(, \frac{3}{7})$ .

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QuestionFind the intercepts of the line given by $-4x + 7y = 3$ . Provide exact values.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given by $-4x +7y =3$ . . The $x$ -intercept of a line is the point where the line crosses the $x$ -axis. At this point, $y =0$ .
3. The $y$ -intercept of a line is the point where the line crosses the $y$ -axis. At this point, $x =0$ .

STEP 2

To find the $x$ -intercept, we set $y =0$ in the equation of the line and solve for $x$ .
$-4x +7(0) =$

STEP 3

implify the equation to find the $x$ -intercept.
$-x =3$

STEP 4

To isolate $x$ , divide both sides of the equation by $-4$ .
$x = \frac{3}{-4}$

STEP 5

Calculate the $x$ -intercept.
$x = -\frac{3}{4}$ So, the $x$ -intercept is $(-\frac{3}{4},0)$ .

STEP 6

To find the $y$ -intercept, we set $x =0$ in the equation of the line and solve for $y$ .
$-4(0) +y =3$

STEP 7

implify the equation to find the $y$ -intercept.
$7y =3$

STEP 8

To isolate $y$ , divide both sides of the equation by $7$ .
$y = \frac{3}{7}$

STEP 9

Calculate the $y$ -intercept.
$y = \frac{3}{7}$ So, the $y$ -intercept is $(, \frac{3}{7})$ .
The $x$ -intercept is $(-\frac{3}{4},)$ and the $y$ -intercept is $(, \frac{3}{7})$ .

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QuestionFind the intercepts of the line given by −4x+7y=3-4x + 7y = 3−4x+7y=3. Provide exact values.

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given by −4x+7y=3-4x +7y =3−4x+7y=3. . The xxx-intercept of a line is the point where the line crosses the xxx-axis. At this point, y=0y =0y=0.3. The yyy-intercept of a line is the point where the line crosses the yyy-axis. At this point, x=0x =0x=0.

STEP 2

To find the xxx-intercept, we set y=0y =0y=0 in the equation of the line and solve for xxx.−4x+7(0)=-4x +7(0) =−4x+7(0)=

STEP 3

implify the equation to find the xxx-intercept.−x=3-x =3−x=3

STEP 4

To isolate xxx, divide both sides of the equation by −4-4−4.x=3−4x = \frac{3}{-4}x=−43​

STEP 5

Calculate the xxx-intercept.x=−34x = -\frac{3}{4}x=−43​So, the xxx-intercept is (−34,0)(-\frac{3}{4},0)(−43​,0).

STEP 6

To find the yyy-intercept, we set x=0x =0x=0 in the equation of the line and solve for yyy.−4(0)+y=3-4(0) +y =3−4(0)+y=3

STEP 7

implify the equation to find the yyy-intercept.7y=37y =37y=3

STEP 8

To isolate yyy, divide both sides of the equation by 777.y=37y = \frac{3}{7}y=73​

STEP 9

Calculate the yyy-intercept.y=37y = \frac{3}{7}y=73​So, the yyy-intercept is (,37)(, \frac{3}{7})(,73​).The xxx-intercept is (−34,)(-\frac{3}{4},)(−43​,) and the yyy-intercept is (,37)(, \frac{3}{7})(,73​).

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QuestionFind the intercepts of the line given by $-4x + 7y = 3$ . Provide exact values.

Assumptions1. The equation of the line is given by $-4x +7y =3$ . . The $x$ -intercept of a line is the point where the line crosses the $x$ -axis. At this point, $y =0$ .
3. The $y$ -intercept of a line is the point where the line crosses the $y$ -axis. At this point, $x =0$ .

To find the $x$ -intercept, we set $y =0$ in the equation of the line and solve for $x$ .
$-4x +7(0) =$

implify the equation to find the $x$ -intercept.
$-x =3$

To isolate $x$ , divide both sides of the equation by $-4$ .
$x = \frac{3}{-4}$

Calculate the $x$ -intercept.
$x = -\frac{3}{4}$ So, the $x$ -intercept is $(-\frac{3}{4},0)$ .

To find the $y$ -intercept, we set $x =0$ in the equation of the line and solve for $y$ .
$-4(0) +y =3$

implify the equation to find the $y$ -intercept.
$7y =3$

To isolate $y$ , divide both sides of the equation by $7$ .
$y = \frac{3}{7}$

Calculate the $y$ -intercept.
$y = \frac{3}{7}$ So, the $y$ -intercept is $(, \frac{3}{7})$ .
The $x$ -intercept is $(-\frac{3}{4},)$ and the $y$ -intercept is $(, \frac{3}{7})$ .