+0  
 
0
81
2
avatar

Write a linear function that passes through both (a,0) and (0,b).

Guest Sep 15, 2017
Sort: 

2+0 Answers

 #1
avatar+1375 
+2

This process is more or less the same when you have 2 arbitrary points (such as (4,6) and (-9,1)). This time, however, we must take into account  that there are variables involved. Let's remind you of slope-intercept form of a line.

 

\(y=mx+b\)

 

 m = slope of the line 

b = y-intercept

 

In this particular case, we know the x- and y-intercepts because those points are given in the original problem. We know that the y-intercept is located at \((0,b)\). Since b is the y-intercept, fill that in! That's the easy bit, I think you'd agree.

 

\(y=mx+b\)

 

We know that the x-intercept is at the point when y=0, so plug that in:
 

\(0=mx+b\) Now, solve for by subtracting b on both sides.
\(-b=mx\) Divide by m on both sides.
\(x=\frac{-b}{m}\)  
   

 

We have determined, with the above algebraic work that when \(y=0,\hspace{1mm}x=\frac{-b}{m}\), which means that the x-intercept is located at \(\left(\frac{-b}{m},0\right)\). However, we also know that the x-intercept is located at \((a,0)\), which means that \(a=\frac{-b}{m}\):

 

\(a=\frac{-b}{m}\) Now, we must solve for m because that is the slope of this linear equation after all.
\(ma=-b\) Divide by a on both sides.
\(m=\frac{-b}{a}\)  
   

 

We now know the value for and for m, so fill it in to get the equation. 

 

\(y=\frac{-b}{a}x+b\)

TheXSquaredFactor  Sep 15, 2017
 #2
avatar+18715 
+3

Creating Linear Equation

Write a linear function that passes through both (a,0) and (0,b).

 

\(\begin{array}{lcll} \dfrac{x}{a} +\dfrac{y}{b} = 1 \begin{array}{rcll} & \text{if } y = 0 \text{ then } x = a \\ & \text{if } x = 0 \text{ then } y = b \\ \end{array} \end{array}\)

 

\(\begin{array}{|rcll|} \hline \frac{x}{a} +\frac{y}{b} &=& 1 \quad & | \quad - \frac{x}{a} \\\\ \frac{y}{b} &=& 1 -\frac{x}{a} \quad & | \quad \cdot b \\\\ y &=& b - \frac{b}{a}\cdot x \\\\ \mathbf{y} &\mathbf{=}& \mathbf{ -\frac{b}{a}\cdot x + b } \\ \hline \end{array}\)

 

laugh

heureka  Sep 15, 2017

8 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details