Chapter 4: Q. 390 (page 537)

In the following exercises, find the equation of a line with a given slope and $y$ -intercept. Write the equation in slope-intercept form.
Slope $- 1$ and $y$ -intercept $(0, 3)$ .

Short Answer

Expert verified

The equation of the line with the given slope $- 1$ and $y$ -intercept $(0, 3)$ is $y = - x + 3$ .

Step by step solution

Step 1. Given data

We have to find the equation of the line.

For that we have,

Slope $(m) = - 1$

$y$ -intercept $= (0, 3)$

Step 2. Equation of the line

We have the point-slope formula $y - y_{1} = m (x - x_{1})$

Where $m$ is the slope and $(x_{1}, y_{1})$ is a point through which the line passes.

Here,

role="math" localid="1647351314106" $\begin{aligned} m = - 1 \\ (x_{1}, y_{1}) = (0, 3) \end{aligned}$

Let us substitute these in the point-slope formula,

That is,

role="math" localid="1647351351191" $\begin{aligned} y - 3 = - 1 (x - 0) \\ y - 3 = - x \dots \dots \dots . (1) \end{aligned}$

Now we have to rewrite this into slope-intercept form, that is $y = m x + b$

Therefore, adding $3$ from both sides of the equation we get,

$\begin{aligned} y - 3 + 3 = - x + 3 \\ y = - x + 3 \end{aligned}$

Hence $y = - x + 3$ is the equation of the line with slope $- 1$ and $y$ -intercept $(0, 3)$ .

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In the following exercises, find the equation of a line with a given slope and $y$ -intercept. Write the equation in slope-intercept form.
Slope $- 1$ and $y$ -intercept $(0, 3)$ .

Short Answer

Step by step solution

Step 1. Given data

Step 2. Equation of the line

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In the following exercises, find the equation of a line with a given slope and y-intercept. Write the equation in slope-intercept form.Slope -1and y-intercept (0,3).

Short Answer

Step by step solution

Step 1. Given data

Step 2. Equation of the line

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Probability and Statistics

Logic and Functions

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, find the equation of a line with a given slope and $y$ -intercept. Write the equation in slope-intercept form.
Slope $- 1$ and $y$ -intercept $(0, 3)$ .