Chapter 5.3, Problem 19P

Write an equation in slope-intercept form of the line that passes through the given points. (3,5) and (0,4)

To determine

To Find: The equation of the line in slope- intercept form passing through points $\left(3,5\right)\&\left(0,4\right)$ .

Answer to Problem 19P

The equation of line in slope intercept form is $y=\frac{1}{3}x+4$ .

Explanation of Solution

Given information:

Line passing through $\left(3,5\right)\&\left(0,4\right)$

Concept and Formula Used:

Equation of line passing through two points is given by $y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)$ . Slope intercept form $y=mx+b$

Calculation:

It is given that line passing through points $\left(3,5\right)\&\left(0,4\right)$

Equation of line through two points is

  $\begin{array}{l}y-y_1=\left(\frac{y_2-y_1}{x_2-x_1}\right)\left(x-x_1\right)\\ \text{where }\left(x_1,y_1\right)=\left(3,5\right)\&\left(x_2,y_2\right)=\left(0,4\right)\\ y-\left(5\right)=\left(\frac{4-\left(5\right)}{0-\left(3\right)}\right)\left(x-3\right)\\ y-5=\left(\frac{-1}{-3}\right)\left(x-3\right)\\ y-5=\frac{1}{3}(x-3)\\ \text{Using distributive property}\\ y-5=\frac{1}{3}x-\frac{1}{3}\times 3\\ y-5=\frac{1}{3}x-1\\ \text{Add 5 on both sides}\\ y-5+5=\frac{1}{3}x-1+5\\ y=\frac{1}{3}x+4\end{array}$

Conclusion:

The equation of line in slope intercept form is $y=\frac{1}{3}x+4$ .