Chapter 1, Problem 21RE

$x\text{-intercept }=2$; containing the point $\left(4,-5\right)$

To determine

To find: The equation of a line having $x\text{-intercept}$ 2 and containing the point $\left(4,-5\right)$. To also sketch a graph of the equation.

Answer to Problem 21RE

Solution:

The general form of equation of the line is $5x+2y=10$.

Explanation of Solution

Given:

The $x\text{-intercept}$ 2 and containing the point $\left(4,-5\right)$. The $x\text{-intercept}$ 2 means the line contains the point $\left(2,0\right)$.

Formula used:

Point slope form of an equation of a line.

$(y-y₁)=m(x-x₁)$

$m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

To find the slope, let $\text{A}=(x,y₁)=\left(2,0\right)$ and $\text{B}=(x,y₂)=\left(4,-5\right)$.

$m=\frac{-5-0}{4-2}$

$=\frac{-5}{2}$

Now using this slope $m=\frac{-5}{2}$ and the point $\text{A}\left(2,0\right)$, the equation can be found.

$y-0=\frac{-5}{2}\left(x-2\right)$

$2y=-5x+10$   Multiply 2 to both sides.

$2y+5x=-5x+10+5x$

$5x+2y=10$

The general form of equation of the line is $5x+2y=10$.