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Complete the table and write the equation

x | y
? | 1.5
-1 | 4
0 | ?
3 | 9
15 | ?


Equation: y = ____ x + _____

User TooAngel
by
8.3k points

2 Answers

6 votes

Answer:

All results in the explanation

Explanation:

To make the equation of the line, we only need two points. Select from the table the points (-1,4) and (3,9).

First, find the slope of the line:

We know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

\begin{gathered}\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\\\end{gathered}m=x2−x1y2−y1

Substituting:

\displaystyle m=\frac{9-4}{3+1}=\frac{5}{4}m=3+19−4=45

This value is used in the slope-point form of the line:

\displaystyle y-k=\frac{5}{4}(x-h)y−k=45(x−h)

Where (h,k) is a point from the table, select for example (3,9):

\displaystyle y-9=\frac{5}{4}(x-3)y−9=45(x−3)

Operate:

\displaystyle y=\frac{5}{4}\cdot x-\frac{5}{4}\cdot 3+9y=45⋅x−45⋅3+9

\displaystyle y=\frac{5}{4}\cdot x+\frac{-15+36}{4}y=45⋅x+4−15+36

The equation of the line is:

\boxed{\displaystyle y=\frac{5}{4}\cdot x+\frac{21}{4}}y=45⋅x+421

Now complete the table.

For x=0:

\displaystyle y=\frac{5}{4}\cdot 0+\frac{21}{4}y=45⋅0+421

y=\frac{21}{4}y=421

For x=15

\displaystyle y=\frac{5}{4}\cdot 15+\frac{21}{4}y=45⋅15+421

\displaystyle y=\frac{75}{4}+\frac{21}{4}=\frac{96}{4}=24y=475+421=496=24

y=24

For y=1.5, find x:

\displaystyle 1.5=\frac{5}{4}\cdot x+\frac{21}{4}1.5=45⋅x+421

Operate:

\displaystyle 1.5-\frac{21}{4}=\frac{5}{4}\cdot x1.5−421=45⋅x

Multiply by 4:

\displaystyle 6-21=5 x6−21=5x

Solve:

x=-15/5=-3x=−15/5=−3

x=-3

User Calimbak
by
8.2k points
2 votes

Answer:

All results in the explanation

Explanation:

To make the equation of the line, we only need two points. Select from the table the points (-1,4) and (3,9).

First, find the slope of the line:

We know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:


\displaystyle m=(y_2-y_1)/(x_2-x_1)\\

Substituting:


\displaystyle m=(9-4)/(3+1)=(5)/(4)

This value is used in the slope-point form of the line:


\displaystyle y-k=(5)/(4)(x-h)

Where (h,k) is a point from the table, select for example (3,9):


\displaystyle y-9=(5)/(4)(x-3)

Operate:


\displaystyle y=(5)/(4)\cdot x-(5)/(4)\cdot 3+9


\displaystyle y=(5)/(4)\cdot x+(-15+36)/(4)

The equation of the line is:


\boxed{\displaystyle y=(5)/(4)\cdot x+(21)/(4)}

Now complete the table.

For x=0:


\displaystyle y=(5)/(4)\cdot 0+(21)/(4)


y=(21)/(4)

For x=15


\displaystyle y=(5)/(4)\cdot 15+(21)/(4)


\displaystyle y=(75)/(4)+(21)/(4)=(96)/(4)=24

y=24

For y=1.5, find x:


\displaystyle 1.5=(5)/(4)\cdot x+(21)/(4)

Operate:


\displaystyle 1.5-(21)/(4)=(5)/(4)\cdot x

Multiply by 4:


\displaystyle 6-21=5 x

Solve:


x=-15/5=-3

x=-3

User Athens Holloway
by
8.2k points

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