Is it possible to solve for $m$ in a linear equation without knowing $b$? Suppose you know certain points on a line say $(5,2)$ up to $(8,10)$ but you don't know exactly where the $y$ intercept would be being somewhere down there at like $-25$ area. How would you solve for $b$ and $m$? Thanks!
 A: You know that $(x,y) = (5,2)$ and $(x,y) = (8,10)$ satisfy the equation $y = mx+b$ where $m$ is the slope of the line and $b$ is the $y$-intercept. This gives you: 
$2 = 5m + b$
$10 = 8m + b$
Now, you have two linear equations and two unknowns. Can you solve for $m$ and $b$?
A: or you use the formula $$m=\frac{y_2-y_1}{x_2-x_1}$$
A: The equation of a line through a point $(x_1,y_1)$ with slope $m$ has equation
$$
y-y_1=m(x-x_1)
$$
A line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ has slope
$$
m=\frac{y_2-y_1}{x_2-x_1}
$$
Thus, the equation of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ has equation
$$
y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\tag{1}
$$
In your case, we have
\begin{align*}
(x_1,y_1) &= (5,2) & (x_2,y_2) &= (8,10)
\end{align*}
Can you plug these points into the equation (1) to obtain your desired equation?
A: Two points determine a line. From the two points you can find the slope by computing the ratio of the differences in $y$ coordinates and in $x$ coordinates. Then you can plug the slope and one of the points into the slope-intercept form of the equation and solve for the $y$-intercept.
A: As the line is passing through the points $(5, 2)$ & $(8, 10)$ hence the equation is given as 
$$y-2=\frac{10-2}{8-5}(x-5)$$ $$y=\frac{8}{3}x-\frac{34}{3}$$ Compare with $y=mx+b$ $$\text{slope}, m=\frac{8}{3}$$$$ \text{y-intercept}, b=-\frac{34}{3}$$
