Solved on Nov 09, 2023

Determine how the graph of $y=-\frac{1}{3}x+3$ changes when it is modified to $y=-\frac{1}{3}x-1$ .

STEP 1

Assumptions1. The original equation is $y=-\frac{1}{3} x+3$ . The new equation is $y=-\frac{1}{3} x-1$
3. The equations represent straight lines in a two-dimensional coordinate system4. The coefficient of $x$ (slope) in both equations is the same, so the lines are parallel5. We are asked to determine how the graph of the equation changes when the constant term changes from3 to -1

STEP 2

The general form of a linear equation is $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept. The y-intercept is the point where the line crosses the y-axis.

STEP 3

In the original equation $y=-\frac{1}{3} x+3$ , the y-intercept is3.

STEP 4

In the new equation $y=-\frac{1}{3} x-1$ , the y-intercept is -1.

STEP 5

The change in the y-intercept from the original equation to the new equation is $-1 -3 = -4$ .

STEP 6

Since the slope of the lines remains the same, the change in the y-intercept means that the line shifts vertically.

Determine how the graph of $y=-\frac{1}{3}x+3$ changes when it is modified to $y=-\frac{1}{3}x-1$ .

STEP 1

STEP 2

The general form of a linear equation is $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept. The y-intercept is the point where the line crosses the y-axis.

STEP 3

In the original equation $y=-\frac{1}{3} x+3$ , the y-intercept is3.

STEP 4

In the new equation $y=-\frac{1}{3} x-1$ , the y-intercept is -1.

STEP 5

The change in the y-intercept from the original equation to the new equation is $-1 -3 = -4$ .

STEP 6

Since the slope of the lines remains the same, the change in the y-intercept means that the line shifts vertically.

STEP 7

A negative change in the y-intercept means the line shifts down.

STEP 8

The line shifts down by4 units.
The line shifts4 units down.

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Determine how the graph of y=−13x+3y=-\frac{1}{3}x+3y=−31​x+3 changes when it is modified to y=−13x−1y=-\frac{1}{3}x-1y=−31​x−1.

STEP 1

STEP 2

The general form of a linear equation is y=mx+cy = mx + cy=mx+c, where mmm is the slope and ccc is the y-intercept. The y-intercept is the point where the line crosses the y-axis.

STEP 3

In the original equation y=−13x+3y=-\frac{1}{3} x+3y=−31​x+3, the y-intercept is3.

STEP 4

In the new equation y=−13x−1y=-\frac{1}{3} x-1y=−31​x−1, the y-intercept is -1.

STEP 5

The change in the y-intercept from the original equation to the new equation is −1−3=−4-1 -3 = -4−1−3=−4.

STEP 6

Since the slope of the lines remains the same, the change in the y-intercept means that the line shifts vertically.

STEP 7

A negative change in the y-intercept means the line shifts down.

STEP 8

The line shifts down by4 units.The line shifts4 units down.

Start learning now

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

Determine how the graph of $y=-\frac{1}{3}x+3$ changes when it is modified to $y=-\frac{1}{3}x-1$ .

The general form of a linear equation is $y = mx + c$ , where $m$ is the slope and $c$ is the y-intercept. The y-intercept is the point where the line crosses the y-axis.

In the original equation $y=-\frac{1}{3} x+3$ , the y-intercept is3.

In the new equation $y=-\frac{1}{3} x-1$ , the y-intercept is -1.

The change in the y-intercept from the original equation to the new equation is $-1 -3 = -4$ .

The line shifts down by4 units.
The line shifts4 units down.