Question

33. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.

Answer 1

Answer:

The linear equation for the line which passes through the points given as (1,5) and (4,11), is written in the point-slope form as y=2x+3.

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (1,5) and (4,11).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 2

Determine the slope of the line.

The points through which the line passes are given as (1,5) and (4,11). Next, the formula for the slope is given as,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substitute 11&5 for $y_{2}$ and $y_{1}$ respectively, and $4 \& 1$ for $x_{2}$ and $x_{1}$ respectively in the above formula. Then simplify to get the slope as follows,

$\begin{aligned}m &=\frac{11-5}{4-1} \\m &=\frac{6}{3} \\m &=2\end{aligned}$

Step 2 of 2

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

$y-y_{1}=m\left(x-x_{1}\right)$

Substitute 2 for $m, 1$ for $x_{1}$, and 5 for $y_{1}$ in the above equation and simplify using the distributive property as follows,

$\begin{aligned}&y-5=2(x-1) \\&y-5=2 x-2 \\&y=2 x-2+5 \\&y=2 x+3\end{aligned}$

This is the required linear equation.