Chapter 3: Q 2. (page 143)

Find an equation of the line containing the points $(1, 4)$ and $(3, 8)$ .

Short Answer

Expert verified

The equation of the line is $\begin{array}{rcl} y & = & 2 x + 2 \end{array}$ .

Step by step solution

Step 1. Given information

The line containing the points $(1, 4)$ and $(3, 8)$ .

Step 2. Find the equation of the line that contain the given points.

The Point-Slope formula with point $(x_{1}, y_{1})$ and the slope $m$ is given by $y - y_{1} = m (x - x_{1})$ , where $m$ is given by $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

Consider the two points as follows:

$\begin{array}{rcl} (x_{1}, y_{1}) & = & (1, 4) \\ (x_{2}, y_{2}) & = & (3, 8) \end{array}$

Find the slope.

$\begin{array}{rcl} m & = & \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\ = & \frac{8 - 4}{3 - 1} \\ = & \frac{4}{2} \\ = & 2 \end{array}$

Thus, the slope is $2$ .

Step 3. Apply the Point-Slope formula to find the equation.

Substitute the value of the point $(x_{1}, y_{1})$ and the slope into the Point-Slope formula.

$\begin{array}{rcl} y - 4 & = & 2 (x - 1) \\ y - 4 & = & 2 x - 2 \\ y & = & 2 x - 2 + 4 \\ y & = & 2 x + 2 \end{array}$

Hence, the equation is $\begin{array}{rcl} y & = & 2 x + 2 \end{array}$ .

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x	$y = f (x)$
-2	$\frac{1}{4}$
-1	$\frac{1}{2}$
0	1
1	2
2	4

Find an equation of the line containing the points $(1, 4)$ and $(3, 8)$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the equation of the line that contain the given points.

Step 3. Apply the Point-Slope formula to find the equation.

One App. One Place for Learning.

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Find an equation of the line containing the points (1,4)and (3,8).

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the equation of the line that contain the given points.

Step 3. Apply the Point-Slope formula to find the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Logic and Functions

Applied Mathematics

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find an equation of the line containing the points $(1, 4)$ and $(3, 8)$ .