QuestionGraph the line given by the equation $y=-\frac{1}{3} x-2$ .

Studdy Solution

STEP 1

Assumptions1. We are graphing the line in a two-dimensional Cartesian coordinate system. . The equation of the line is given by $y=-\frac{1}{3} x-$ .

STEP 2

The equation of the line is in the slope-intercept form $y=mx+b$ , where $m$ is the slope of the line and $b$ is the y-intercept. In this case, $m=-\frac{1}{}$ and $b=-2$ .

STEP 3

The y-intercept $b=-2$ is the point where the line crosses the y-axis. This means our line crosses the y-axis at the point $(0, -2)$ .

STEP 4

The slope $m=-\frac{1}{3}$ tells us how steep the line is. A slope of $-\frac{1}{3}$ means that for every3 units we move to the right along the x-axis, we move1 unit down along the y-axis.

STEP 5

Starting from the y-intercept $(0, -2)$ , move3 units to the right to $x=3$ , and then1 unit down to $y=-3$ . This gives us another point on the line, $(3, -3)$ .

STEP 6

Plot the points $(0, -2)$ and $(3, -3)$ on the Cartesian plane.

STEP 7

Draw a straight line through the points $(0, -2)$ and $(3, -3)$ . This line represents the graph of the equation $y=-\frac{1}{3} x-2$ .

Was this helpful?

QuestionGraph the line given by the equation $y=-\frac{1}{3} x-2$ .

Studdy Solution

STEP 1

Assumptions1. We are graphing the line in a two-dimensional Cartesian coordinate system. . The equation of the line is given by $y=-\frac{1}{3} x-$ .

STEP 2

The equation of the line is in the slope-intercept form $y=mx+b$ , where $m$ is the slope of the line and $b$ is the y-intercept. In this case, $m=-\frac{1}{}$ and $b=-2$ .

STEP 3

The y-intercept $b=-2$ is the point where the line crosses the y-axis. This means our line crosses the y-axis at the point $(0, -2)$ .

STEP 4

The slope $m=-\frac{1}{3}$ tells us how steep the line is. A slope of $-\frac{1}{3}$ means that for every3 units we move to the right along the x-axis, we move1 unit down along the y-axis.

STEP 5

Starting from the y-intercept $(0, -2)$ , move3 units to the right to $x=3$ , and then1 unit down to $y=-3$ . This gives us another point on the line, $(3, -3)$ .

STEP 6

Plot the points $(0, -2)$ and $(3, -3)$ on the Cartesian plane.

STEP 7

Draw a straight line through the points $(0, -2)$ and $(3, -3)$ . This line represents the graph of the equation $y=-\frac{1}{3} x-2$ .

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.

QuestionGraph the line given by the equation y=−13x−2y=-\frac{1}{3} x-2y=−31​x−2.

Studdy Solution

STEP 1

Assumptions1. We are graphing the line in a two-dimensional Cartesian coordinate system. . The equation of the line is given by y=−13x−y=-\frac{1}{3} x-y=−31​x−.

STEP 2

The equation of the line is in the slope-intercept form y=mx+by=mx+by=mx+b, where mmm is the slope of the line and bbb is the y-intercept. In this case, m=−1m=-\frac{1}{}m=−1​ and b=−2b=-2b=−2.

STEP 3

The y-intercept b=−2b=-2b=−2 is the point where the line crosses the y-axis. This means our line crosses the y-axis at the point (0,−2)(0, -2)(0,−2).

STEP 4

The slope m=−13m=-\frac{1}{3}m=−31​ tells us how steep the line is. A slope of −13-\frac{1}{3}−31​ means that for every3 units we move to the right along the x-axis, we move1 unit down along the y-axis.

STEP 5

Starting from the y-intercept (0,−2)(0, -2)(0,−2), move3 units to the right to x=3x=3x=3, and then1 unit down to y=−3y=-3y=−3. This gives us another point on the line, (3,−3)(3, -3)(3,−3).

STEP 6

Plot the points (0,−2)(0, -2)(0,−2) and (3,−3)(3, -3)(3,−3) on the Cartesian plane.

STEP 7

Draw a straight line through the points (0,−2)(0, -2)(0,−2) and (3,−3)(3, -3)(3,−3). This line represents the graph of the equation y=−13x−2y=-\frac{1}{3} x-2y=−31​x−2.

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.

QuestionGraph the line given by the equation $y=-\frac{1}{3} x-2$ .

Assumptions1. We are graphing the line in a two-dimensional Cartesian coordinate system. . The equation of the line is given by $y=-\frac{1}{3} x-$ .

The equation of the line is in the slope-intercept form $y=mx+b$ , where $m$ is the slope of the line and $b$ is the y-intercept. In this case, $m=-\frac{1}{}$ and $b=-2$ .

The y-intercept $b=-2$ is the point where the line crosses the y-axis. This means our line crosses the y-axis at the point $(0, -2)$ .

The slope $m=-\frac{1}{3}$ tells us how steep the line is. A slope of $-\frac{1}{3}$ means that for every3 units we move to the right along the x-axis, we move1 unit down along the y-axis.

Starting from the y-intercept $(0, -2)$ , move3 units to the right to $x=3$ , and then1 unit down to $y=-3$ . This gives us another point on the line, $(3, -3)$ .

Plot the points $(0, -2)$ and $(3, -3)$ on the Cartesian plane.

Draw a straight line through the points $(0, -2)$ and $(3, -3)$ . This line represents the graph of the equation $y=-\frac{1}{3} x-2$ .