Solved on Sep 19, 2023

Graph the linear equation $y = -\frac{5}{2}x + 3$ and find at least 5 solutions in the table of values.

STEP 1

Assumptions1. The equation is linear and in two variables, x and y. . The equation is in the form y = mx + c, where m is the slope and c is the y-intercept.
3. The slope of the line is -5/ and the y-intercept is3.
4. We need to find at least five solutions for the equation.

STEP 2

First, let's find the y-values when x is0,1,2,, and4. We can do this by substituting these x-values into the equation and solving for y.
$y = -\frac{5}{2} x +$

STEP 3

When x =0, the equation becomes $y = -\frac{5}{2} \cdot0 +3$

STEP 4

olve for y when x =0.
$y =0 +3 =3$

STEP 5

When x =1, the equation becomes $y = -\frac{5}{2} \cdot1 +3$

STEP 6

olve for y when x =1.
$y = -\frac{5}{2} +3 = -\frac{2}{2} = -1$

STEP 7

When x =2, the equation becomes $y = -\frac{5}{2} \cdot2 +3$

STEP 8

olve for y when x =2.
$y = -5 +3 = -2$

STEP 9

When x =3, the equation becomes $y = -\frac{5}{2} \cdot3 +3$

STEP 10

olve for y when x =3.
$y = -\frac{15}{2} +3 = -\frac{9}{2} = -4.5$

STEP 11

When x =4, the equation becomes $y = -\frac{5}{} \cdot4 +3$

STEP 12

olve for y when x =4.
$y = -10 + = -7$

STEP 13

Now, we have five solutions for the equation. (0,3)
2. (, -)
3. (2, -2) . (3, -.5)
5. (, -7)

STEP 14

Next, we will graph the equation. Plot the y-intercept (0,3) on the graph first.

STEP 15

Then, use the slope (-5/2) to find the next point. The slope is the change in y divided by the change in x. So, from the y-intercept, move down5 units and to the right2 units to plot the next point.

STEP 16

Repeat this process to plot the remaining points.

STEP 17

Finally, draw a line through the points to represent the equation.
The graph of the equation $y = -\frac{5}{2}x +3$ and the five solutions are as follows. (0,3)
2. (, -)
3. (2, -2)
4. (3, -4.5)
5. (4, -7)

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Graph the linear equation $y = -\frac{5}{2}x + 3$ and find at least 5 solutions in the table of values.

STEP 1

Assumptions1. The equation is linear and in two variables, x and y. . The equation is in the form y = mx + c, where m is the slope and c is the y-intercept.
3. The slope of the line is -5/ and the y-intercept is3.
4. We need to find at least five solutions for the equation.

STEP 2

First, let's find the y-values when x is0,1,2,, and4. We can do this by substituting these x-values into the equation and solving for y.
$y = -\frac{5}{2} x +$

STEP 3

When x =0, the equation becomes $y = -\frac{5}{2} \cdot0 +3$

STEP 4

olve for y when x =0.
$y =0 +3 =3$

STEP 5

When x =1, the equation becomes $y = -\frac{5}{2} \cdot1 +3$

STEP 6

olve for y when x =1.
$y = -\frac{5}{2} +3 = -\frac{2}{2} = -1$

STEP 7

When x =2, the equation becomes $y = -\frac{5}{2} \cdot2 +3$

STEP 8

olve for y when x =2.
$y = -5 +3 = -2$

STEP 9

When x =3, the equation becomes $y = -\frac{5}{2} \cdot3 +3$

STEP 10

olve for y when x =3.
$y = -\frac{15}{2} +3 = -\frac{9}{2} = -4.5$

STEP 11

When x =4, the equation becomes $y = -\frac{5}{} \cdot4 +3$

STEP 12

olve for y when x =4.
$y = -10 + = -7$

STEP 13

Now, we have five solutions for the equation. (0,3)
2. (, -)
3. (2, -2) . (3, -.5)
5. (, -7)

STEP 14

Next, we will graph the equation. Plot the y-intercept (0,3) on the graph first.

STEP 15

Then, use the slope (-5/2) to find the next point. The slope is the change in y divided by the change in x. So, from the y-intercept, move down5 units and to the right2 units to plot the next point.

STEP 16

Repeat this process to plot the remaining points.

STEP 17

Finally, draw a line through the points to represent the equation.
The graph of the equation $y = -\frac{5}{2}x +3$ and the five solutions are as follows. (0,3)
2. (, -)
3. (2, -2)
4. (3, -4.5)
5. (4, -7)

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Graph the linear equation y=−52x+3y = -\frac{5}{2}x + 3y=−25​x+3 and find at least 5 solutions in the table of values.

STEP 1

Assumptions1. The equation is linear and in two variables, x and y. . The equation is in the form y = mx + c, where m is the slope and c is the y-intercept.3. The slope of the line is -5/ and the y-intercept is3.4. We need to find at least five solutions for the equation.

STEP 2

First, let's find the y-values when x is0,1,2,, and4. We can do this by substituting these x-values into the equation and solving for y.y=−52x+y = -\frac{5}{2} x +y=−25​x+

STEP 3

When x =0, the equation becomesy=−52⋅0+3y = -\frac{5}{2} \cdot0 +3y=−25​⋅0+3

STEP 4

olve for y when x =0.y=0+3=3y =0 +3 =3y=0+3=3

STEP 5

When x =1, the equation becomesy=−52⋅1+3y = -\frac{5}{2} \cdot1 +3y=−25​⋅1+3

STEP 6

olve for y when x =1.y=−52+3=−22=−1y = -\frac{5}{2} +3 = -\frac{2}{2} = -1y=−25​+3=−22​=−1

STEP 7

When x =2, the equation becomesy=−52⋅2+3y = -\frac{5}{2} \cdot2 +3y=−25​⋅2+3

STEP 8

olve for y when x =2.y=−5+3=−2y = -5 +3 = -2y=−5+3=−2

STEP 9

When x =3, the equation becomesy=−52⋅3+3y = -\frac{5}{2} \cdot3 +3y=−25​⋅3+3

STEP 10

olve for y when x =3.y=−152+3=−92=−4.5y = -\frac{15}{2} +3 = -\frac{9}{2} = -4.5y=−215​+3=−29​=−4.5

STEP 11

When x =4, the equation becomesy=−5⋅4+3y = -\frac{5}{} \cdot4 +3y=−5​⋅4+3

STEP 12

olve for y when x =4.y=−10+=−7y = -10 + = -7y=−10+=−7

STEP 13

Now, we have five solutions for the equation. (0,3)2. (, -)3. (2, -2) . (3, -.5)5. (, -7)

STEP 14

Next, we will graph the equation. Plot the y-intercept (0,3) on the graph first.

STEP 15

Then, use the slope (-5/2) to find the next point. The slope is the change in y divided by the change in x. So, from the y-intercept, move down5 units and to the right2 units to plot the next point.

STEP 16

Repeat this process to plot the remaining points.

STEP 17

Finally, draw a line through the points to represent the equation.The graph of the equation y=−52x+3y = -\frac{5}{2}x +3y=−25​x+3 and the five solutions are as follows. (0,3)2. (, -)3. (2, -2)4. (3, -4.5)5. (4, -7)

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

Graph the linear equation $y = -\frac{5}{2}x + 3$ and find at least 5 solutions in the table of values.

Assumptions1. The equation is linear and in two variables, x and y. . The equation is in the form y = mx + c, where m is the slope and c is the y-intercept.
3. The slope of the line is -5/ and the y-intercept is3.
4. We need to find at least five solutions for the equation.

First, let's find the y-values when x is0,1,2,, and4. We can do this by substituting these x-values into the equation and solving for y.
$y = -\frac{5}{2} x +$

When x =0, the equation becomes $y = -\frac{5}{2} \cdot0 +3$

olve for y when x =0.
$y =0 +3 =3$

When x =1, the equation becomes $y = -\frac{5}{2} \cdot1 +3$

olve for y when x =1.
$y = -\frac{5}{2} +3 = -\frac{2}{2} = -1$

When x =2, the equation becomes $y = -\frac{5}{2} \cdot2 +3$

olve for y when x =2.
$y = -5 +3 = -2$

When x =3, the equation becomes $y = -\frac{5}{2} \cdot3 +3$

olve for y when x =3.
$y = -\frac{15}{2} +3 = -\frac{9}{2} = -4.5$

When x =4, the equation becomes $y = -\frac{5}{} \cdot4 +3$

olve for y when x =4.
$y = -10 + = -7$

Now, we have five solutions for the equation. (0,3)
2. (, -)
3. (2, -2) . (3, -.5)
5. (, -7)

Finally, draw a line through the points to represent the equation.
The graph of the equation $y = -\frac{5}{2}x +3$ and the five solutions are as follows. (0,3)
2. (, -)
3. (2, -2)
4. (3, -4.5)
5. (4, -7)