Question Find the equation of a line with slope -2.

Studdy Solution

STEP 1

Assumptions
1. We are given a linear equation in two variables, $x$ and $y$ .
2. The equation is $y = -2x$ .
3. We are likely asked to analyze or graph this equation.

STEP 2

Identify the slope and y-intercept of the equation.
The general form of a linear equation is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 3

Compare the given equation $y = -2x$ with the general form to find the slope and y-intercept.
The slope $m = -2$ and the y-intercept $b = 0$ .

STEP 4

Interpret the slope.
The slope $m = -2$ means that for every unit increase in $x$ , $y$ decreases by 2 units.

STEP 5

Interpret the y-intercept.
The y-intercept $b = 0$ means that the line crosses the y-axis at the origin (0,0).

STEP 6

If we want to graph the equation, we can start at the y-intercept (0,0) and use the slope to find another point.

STEP 7

Since the slope is -2, we can move 1 unit to the right (positive x-direction) and 2 units down (negative y-direction) from the origin to find a second point on the line.

STEP 8

The second point using the slope would be (1, -2).

STEP 9

Plot the two points (0,0) and (1, -2) on a coordinate plane.

STEP 10

Draw a straight line through the two points to graph the equation $y = -2x$ .
This line represents all the solutions to the equation $y = -2x$ .

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Question Find the equation of a line with slope -2.

Studdy Solution

STEP 1

Assumptions
1. We are given a linear equation in two variables, $x$ and $y$ .
2. The equation is $y = -2x$ .
3. We are likely asked to analyze or graph this equation.

STEP 2

Identify the slope and y-intercept of the equation.
The general form of a linear equation is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 3

Compare the given equation $y = -2x$ with the general form to find the slope and y-intercept.
The slope $m = -2$ and the y-intercept $b = 0$ .

STEP 4

Interpret the slope.
The slope $m = -2$ means that for every unit increase in $x$ , $y$ decreases by 2 units.

STEP 5

Interpret the y-intercept.
The y-intercept $b = 0$ means that the line crosses the y-axis at the origin (0,0).

STEP 6

If we want to graph the equation, we can start at the y-intercept (0,0) and use the slope to find another point.

STEP 7

Since the slope is -2, we can move 1 unit to the right (positive x-direction) and 2 units down (negative y-direction) from the origin to find a second point on the line.

STEP 8

The second point using the slope would be (1, -2).

STEP 9

Plot the two points (0,0) and (1, -2) on a coordinate plane.

STEP 10

Draw a straight line through the two points to graph the equation $y = -2x$ .
This line represents all the solutions to the equation $y = -2x$ .

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Question Find the equation of a line with slope -2.

Studdy Solution

STEP 1

Assumptions1. We are given a linear equation in two variables, x x x and y y y.2. The equation is y=−2x y = -2x y=−2x.3. We are likely asked to analyze or graph this equation.

STEP 2

Identify the slope and y-intercept of the equation.The general form of a linear equation is y=mx+b y = mx + b y=mx+b, where m m m is the slope and b b b is the y-intercept.

STEP 3

Compare the given equation y=−2x y = -2x y=−2x with the general form to find the slope and y-intercept.The slope m=−2 m = -2 m=−2 and the y-intercept b=0 b = 0 b=0.

STEP 4

Interpret the slope.The slope m=−2 m = -2 m=−2 means that for every unit increase in x x x, y y y decreases by 2 units.

STEP 5

Interpret the y-intercept.The y-intercept b=0 b = 0 b=0 means that the line crosses the y-axis at the origin (0,0).

STEP 6

If we want to graph the equation, we can start at the y-intercept (0,0) and use the slope to find another point.

STEP 7

Since the slope is -2, we can move 1 unit to the right (positive x-direction) and 2 units down (negative y-direction) from the origin to find a second point on the line.

STEP 8

The second point using the slope would be (1, -2).

STEP 9

Plot the two points (0,0) and (1, -2) on a coordinate plane.

STEP 10

Draw a straight line through the two points to graph the equation y=−2x y = -2x y=−2x.This line represents all the solutions to the equation y=−2x y = -2x y=−2x.

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Assumptions
1. We are given a linear equation in two variables, $x$ and $y$ .
2. The equation is $y = -2x$ .
3. We are likely asked to analyze or graph this equation.

Identify the slope and y-intercept of the equation.
The general form of a linear equation is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

Compare the given equation $y = -2x$ with the general form to find the slope and y-intercept.
The slope $m = -2$ and the y-intercept $b = 0$ .

Interpret the slope.
The slope $m = -2$ means that for every unit increase in $x$ , $y$ decreases by 2 units.

Interpret the y-intercept.
The y-intercept $b = 0$ means that the line crosses the y-axis at the origin (0,0).

Draw a straight line through the two points to graph the equation $y = -2x$ .
This line represents all the solutions to the equation $y = -2x$ .