Solveeit Logo

Question

Question: How do you solve for \(t\) in \(a = p + prt?\)...

How do you solve for tt in a=p+prt?a = p + prt?

Explanation

Solution

As we know that the above given equation a=p+prta = 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=CAx + By = C . When an equation is given in this form it’s also pretty easy to find both intercepts (x,y)(x,y). By transferring the positive aa 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 tt we need to isolate the term containing tt on the left hand side i.e. to simplify a=p+prta = p + prt and solving for variable tt , move all the terms containing p,rp,r to the right.
Here we will transfer the +p + p to the right hand side and we get ap=prta - p = prt.
Now since both pp and rr are being multiplied in left hand side, so when we will transfer it to the right hand side it will turn into division: appr=t\dfrac{{a - p}}{{pr}} = t. It can also be written as
aprppr=t\dfrac{a}{{pr}} - \dfrac{p}{{pr}} = t.
Hence the required value of tt is appr\dfrac{{a - p}}{{pr}}.

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=CAx + By = C ,AA and BBare real numbers and CC is a constant, it can be equal to zero(0)(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 11 . The slope intercept form of a linear equation is y=mx+cy = mx + c ,where mm is the slope of the line and bb in the equation is the y-intercept and xx and yy are the coordinates of x- axis and y-axis , respectively.