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Completion requirements
Determine the slope and \(y\)-intercept of the linear function represented on the graph below. Then, write the equation of the line.
Choose two points on the graph to determine slope, such as \((0, 15)\) and \((10, 45)\).
In this case, the slope is \(3\) m/s.
The \(y\)-intercept is found where the line intersects the \(y\)-axis, or where \(x = 0\).
For this graph, the \(y\)-intercept is \(15\), or \((0, 15)\).
The equation of the line is \(\begin{align}&y = mx + b \\
&y = 3x + 15
\end{align} \).
\[\begin {align}
m &= \frac{{y_2 - y_1 }}{{x_2 - x_1 }} \\
m &= \frac{{45 - 15}}{{10 - 0}} \\
m &= \frac{{30}}{{10}} \\
m &= 3 \end {align}\]
m &= \frac{{y_2 - y_1 }}{{x_2 - x_1 }} \\
m &= \frac{{45 - 15}}{{10 - 0}} \\
m &= \frac{{30}}{{10}} \\
m &= 3 \end {align}\]
In this case, the slope is \(3\) m/s.
The \(y\)-intercept is found where the line intersects the \(y\)-axis, or where \(x = 0\).
For this graph, the \(y\)-intercept is \(15\), or \((0, 15)\).
The equation of the line is \(\begin{align}&y = mx + b \\
&y = 3x + 15
\end{align} \).