QuestionUne
\begin{tabular}{|c|c|}
\hline & \\
\hline 2 & 7 \\
\hline 4 & 10.5 \\
\hline 7 & 15.75 \\
\hline 11 & 22.75 \\
\hline
\end{tabular}
Line
\begin{tabular}{|r|r|}
\hline & \multicolumn{1}{|c|}{} \\
\hline-3 & 4 \\
\hline-2 & 0 \\
\hline 1 & -12 \\
\hline 4 & -24 \\
\hline
\end{tabular}
Write a system of equations that represents lines fand . (work space below)
Studdy Solution
STEP 1
1. We are given two sets of points for two lines, and .
2. We need to find the equations of these lines in the form , where is the slope and is the y-intercept.
3. The points are assumed to lie on straight lines.
STEP 2
1. Determine the equation of line using the given points.
2. Determine the equation of line using the given points.
STEP 3
Calculate the slope of line using two points from the table. Let's use the points and .
The formula for the slope is:
Substitute the values:
STEP 4
Use the slope and one of the points, say , to find the y-intercept .
The equation of the line is:
Substitute , , and :
The equation of line is:
STEP 5
Calculate the slope of line using two points from the table. Let's use the points and .
The formula for the slope is:
Substitute the values:
STEP 6
Use the slope and one of the points, say , to find the y-intercept .
The equation of the line is:
Substitute , , and :
The equation of line is:
The system of equations representing lines and is:
\[
\begin{align*}
f: & \quad y = 1.75x + 3.5 \\
g: & \quad y = -4x - 8 \\
\end{align*}$
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