First, you should plug the given points, (5, –8) (–2, 6), into the slope formula to find the slope of the line. 

$\displaystyle slope=\frac{y_2-y_1}{x_2-x_1}$

$\displaystyle slope=\frac{-8-6}{5-(-2)}=\frac{-8-6}{5+2}=\frac{-14}{7}=-2$

Then, plug the slope into the slope formula, y = mx + b, where m is the slope.

y = –2x + b

Plug in either one of the given points, (5, –8) or (–2, 6), into the equation to find the y-intercept (b). 

6 = –2(–2) + b

6 = 4 + b

2 = b

Plug in both the slope and the y-intercept into slope intercept form. 

y = –2x + 2

These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.

m = 3 and b = –5

$\displaystyle y=mx+b$ is the slope-intercept form of the equation of a line.

Slope $\displaystyle m$ is equal to $\displaystyle \frac{rise}{run}$ between points, or $\displaystyle \frac{6}{-12}$.

So $\displaystyle m=-\frac{1}{2}$.

At point (8, 3 ) the equation becomes

$\displaystyle 3=-\frac{1}{2}\cdot 8+b\rightarrow 3=-4+b$

So $\displaystyle b=7$

The slope of the line passing through points $\displaystyle A$ and $\displaystyle B$ can be computed as follows:

$\displaystyle Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{5-2}{1-0}=3$

Now, the new line, since it is parallel, will have the same slope.  To find the equation of this new line, we use point-slope form:

$\displaystyle y-y_{1}=m(x-x_{1})$, where $\displaystyle m$ is the slope and $\displaystyle \left ( x_{1},y_{1} \right )$ is the point the line passes through.

$\displaystyle y-(-5)=3(x-(-3))$

$\displaystyle y+5-3(x+3)$

$\displaystyle y+5=3x+9$

After rearranging, this becomes $\displaystyle 3x-y=-4$

When finding the equation of a line from some of its points, it's easiest to first find the line's slope, or $\displaystyle m$.

To find slope, divide the difference in $\displaystyle y$ values by the difference in $\displaystyle x$ values. This gives us $\displaystyle 3$ divided by $\displaystyle -6$, or $\displaystyle -\frac{1}{2}$.

Next, we just need to find $\displaystyle b$, which is the line's $\displaystyle y$-intercept. By plugging one of the points into the equation $\displaystyle y = -\frac{1}{2}x+b$, we obtain a $\displaystyle b$ value of 11 and a final equation of

$\displaystyle y=-\frac{1}{2}x+11$

We can find the equation of th line in slope-intercept form by finding $\displaystyle m$ and $\displaystyle b$.

First, calculate the slope, $\displaystyle m$, for any two points. We will use the first two.

$\displaystyle m=\frac{y_{2}-y_1}{x_2-x_1}=\frac{7-4}{1-0}=\frac{3}{1}=3$

Next, using the slope and any point on the line, calculate the y-intercept, $\displaystyle b$. We will use the first point.

$\displaystyle y=mx+b$

$\displaystyle 4=3(0)+b$

$\displaystyle 4=b$

The correct equation in slope-intercept form is $\displaystyle y=3x+4$.

When a line is in the $\displaystyle y=mx+b$ format, the $\displaystyle m$ is its slope and the $\displaystyle b$ is its $\displaystyle y$-intercept. In this case, the equation with a slope of $\displaystyle 2$ and a $\displaystyle y$-intercept of $\displaystyle -12$ is $\displaystyle y=2x-12$.

We can treat the price of the stock as the $\displaystyle y$ value and the year as the $\displaystyle x$ value, making any points take the form $\displaystyle (year, price)$, or $\displaystyle (x,p)$. This question is asking for the line that includes points $\displaystyle (1990,27.17)$ and $\displaystyle (2000,48.93)$. 

To find the equation, first, we need the slope.

$\displaystyle m= \frac{48.93-27.17}{2000-1990}= \frac{21.76}{10}=2.176$

Now use the point-slope formula with this slope and either point (we will choose the second).

$\displaystyle y-48.93 = 2.176(x-2000)$

$\displaystyle y-48.93 = 2.176x-4352$

$\displaystyle y = 2.176x-4303.07$

$\displaystyle \textup{Equation of a line is }y=mx+b \textup{, where }m\textup{ is the slope and }b\textup{ is the }y\textup{-intercept.}$

$\displaystyle \textup{Find slope} = \frac{\Delta y}{\Delta x}=\frac{2-4}{-2--6}=\frac{-2}{4}=\frac{-1}{2}$

$\displaystyle \textup{Use slope to find }y\textup{-intercept:} \frac{-1}{2}= \frac{b-2}{0--2}\;\;\;\;\frac{-1}{2}=\frac{b-2}{2}$

$\displaystyle 2b-4 = -2\;\;\;\;\;\;2b = 2\;\;\;\;\;b=1$

$\displaystyle y=\frac{-x}{2}+1$

When an equation is in the $\displaystyle y=mx+b$ form, the $\displaystyle m$ indicates its slope while the $\displaystyle b$ indicates its $\displaystyle y$-intercept. In this case, we are looking for a line with a $\displaystyle m$ of 5 and a $\displaystyle b$ of 6, or $\displaystyle y=5x+6$.