Question Solve $x-y<2$ for $y$ , find slope and $y$ -intercept, determine if line is dashed or solid, and identify shading.

Studdy Solution

STEP 1

Assumptions1. The inequality is $x-y<$ . We are solving for $y$
3. We need to find the slope and y-intercept4. We need to determine if the line is dashed or solid5. We need to identify whether the shading is above or below the line

STEP 2

First, we need to isolate $y$ on one side of the inequality. To do this, we will subtract $x$ from both sides.
$x - y <2$ $-y <2 - x$

STEP 3

To get $y$ by itself, we will multiply both sides by $-1$ . Remember that when you multiply or divide an inequality by a negative number, you must flip the inequality sign.
$y > x -2$

STEP 4

Now we have the inequality in slope-intercept form, $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. In this case, $m =1$ and $b = -2$ .

STEP 5

The inequality sign is "greater than", so the line will be dashed. If the inequality sign was "greater than or equal to", the line would be solid.

STEP 6

Because the inequality is $y > x -2$ , the shading will be above the line. If the inequality was $y < x -2$ , the shading would be below the line.
So, the solution to the inequality is $y > x -2$ , the slope is1, the y-intercept is -2, the line is dashed, and the shading is above the line.

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Question Solve $x-y<2$ for $y$ , find slope and $y$ -intercept, determine if line is dashed or solid, and identify shading.

Studdy Solution

STEP 1

Assumptions1. The inequality is $x-y<$ . We are solving for $y$
3. We need to find the slope and y-intercept4. We need to determine if the line is dashed or solid5. We need to identify whether the shading is above or below the line

STEP 2

First, we need to isolate $y$ on one side of the inequality. To do this, we will subtract $x$ from both sides.
$x - y <2$ $-y <2 - x$

STEP 3

To get $y$ by itself, we will multiply both sides by $-1$ . Remember that when you multiply or divide an inequality by a negative number, you must flip the inequality sign.
$y > x -2$

STEP 4

Now we have the inequality in slope-intercept form, $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. In this case, $m =1$ and $b = -2$ .

STEP 5

The inequality sign is "greater than", so the line will be dashed. If the inequality sign was "greater than or equal to", the line would be solid.

STEP 6

Because the inequality is $y > x -2$ , the shading will be above the line. If the inequality was $y < x -2$ , the shading would be below the line.
So, the solution to the inequality is $y > x -2$ , the slope is1, the y-intercept is -2, the line is dashed, and the shading is above the line.

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Question Solve x−y<2x-y<2x−y<2 for yyy, find slope and yyy-intercept, determine if line is dashed or solid, and identify shading.

Studdy Solution

STEP 1

Assumptions1. The inequality is x−y<x-y<x−y< . We are solving for yyy3. We need to find the slope and y-intercept4. We need to determine if the line is dashed or solid5. We need to identify whether the shading is above or below the line

STEP 2

First, we need to isolate yyy on one side of the inequality. To do this, we will subtract xxx from both sides.x−y<2x - y <2x−y<2−y<2−x-y <2 - x−y<2−x

STEP 3

To get yyy by itself, we will multiply both sides by −1-1−1. Remember that when you multiply or divide an inequality by a negative number, you must flip the inequality sign.y>x−2y > x -2y>x−2

STEP 4

Now we have the inequality in slope-intercept form, y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept. In this case, m=1m =1m=1 and b=−2b = -2b=−2.

STEP 5

The inequality sign is "greater than", so the line will be dashed. If the inequality sign was "greater than or equal to", the line would be solid.

STEP 6

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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.

Question Solve $x-y<2$ for $y$ , find slope and $y$ -intercept, determine if line is dashed or solid, and identify shading.

Assumptions1. The inequality is $x-y<$ . We are solving for $y$
3. We need to find the slope and y-intercept4. We need to determine if the line is dashed or solid5. We need to identify whether the shading is above or below the line

First, we need to isolate $y$ on one side of the inequality. To do this, we will subtract $x$ from both sides.
$x - y <2$ $-y <2 - x$

To get $y$ by itself, we will multiply both sides by $-1$ . Remember that when you multiply or divide an inequality by a negative number, you must flip the inequality sign.
$y > x -2$

Now we have the inequality in slope-intercept form, $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. In this case, $m =1$ and $b = -2$ .