### 11.3.1 Straight Lines

This subsection is not completed yet, but in the meantime here are some practice questions.

Remember:
Slope, which is usually given the letter $m$, is a measure of the steepness of a line. It is the number of units up or down for every unit across, and can be calculated by dividing the rise by the run. A line connecting two points $(x_1,y_1)$ and $(x_2,y_2)$ will have a rise of $\Delta y = y_2 - y_1$ and a run of $\Delta x = x_2 - x_1$, with a slope of: $m = \frac{\Delta y}{\Delta x}$

Remember:
The steeper the line, the bigger the slope, $m$. A slope of $1$ is on a $45^\circ$ angle. A slope of $0$ will be horizontal. If the line is sloping downwards then either $\Delta y$ or $\Delta x$ will be negative, and so will the slope, $m$.

Remember:
To find the slope of a line given its equation, rewrite it in the form $y=mx + c$. For example, \begin{align*} y &= 2 + x\\ &= 1x + 2\\ m &= 1 \end{align*} \begin{align*} y &= 5 - \frac{x}{2}\\ &= -\frac{1}{2} x + 5\\ m &= -\frac{1}{2} \end{align*} \begin{align*} 2x + y + 3 &= 0\\ y &= -2x - 3\\ m &= -2 \end{align*}

Remember:
If a line with slope $m_1$ is perpendicular to another line with slope $m_2$ then $m_1 m_2 = -1$

Remember:
To find the y-intercept of a straight line (which is the $c$ in $y = mx + c$), knowing its slope, $m$, and a point on the line, $(x_1,y_1)$, there are a couple methods. You can say: $y-y_1 = m(x-x_1)$ and then solve for $y$ to get it into the form $y = mx + c$. Or you could sub $(x_1,y_1)$ into the equation $y=mx+c$ to get: $y_1 = mx_1 + c$ and then solve for $c$. In either case, $c = y_1 - mx_1$ will be the conclusion.