Question
Question: How do you solve for \(t\) in \(a = p + prt?\)...
How do you solve for t in a=p+prt?
Solution
As we know that the above given equation a=p+prt is a linear equation. An equation for a straight line is called a linear equation. The standard form of linear equations in two variables is Ax+By=C . When an equation is given in this form it’s also pretty easy to find both intercepts (x,y). By transferring the positive a to the right hand side value gives the required solution.
Complete step by step solution:
As we know that the above given equation is a linear equation and to solve for t we need to isolate the term containing t on the left hand side i.e. to simplify a=p+prt and solving for variable t , move all the terms containing p,r to the right.
Here we will transfer the +p to the right hand side and we get a−p=prt.
Now since both p and r are being multiplied in left hand side, so when we will transfer it to the right hand side it will turn into division: pra−p=t. It can also be written as
pra−prp=t.
Hence the required value of t is pra−p.
Note: We should keep in mind the positive and negative signs while calculating the value of any variable as it will change it’s slope and value. In the equation Ax+By=C ,A and Bare real numbers and C is a constant, it can be equal to zero(0) also. These types of equations are of first order. Linear equations are also first-degree equations as it has the highest exponent of variables as 1 . The slope intercept form of a linear equation is y=mx+c ,where m is the slope of the line and b in the equation is the y-intercept and x and y are the coordinates of x- axis and y-axis , respectively.