Chapter 2: Q25. (page 79)

Write an equation in slope-intercept form for the line that satisfies each set of conditions.
Slope $- \frac{1}{2}$ , passes through $(1, 3)$

Short Answer

Expert verified

The equation of the required straight line in slope-intercept form is $y = - \frac{1}{2} x + \frac{7}{2}$ .

Step by step solution

– State the concept

The slope intercept form of a straight-line equation is $y = m x + c$ where $m$ is the slope and $c$ is the y-intercept.

The equation of a straight-line having slope $m$ and passing through the point $(h, k)$ is given as $y - k = m (x - h)$ .

– List the given data

It is given that the slope of the line is $- \frac{1}{2}$ and the line passes through $(1, 3)$ .

Then, $m = - \frac{1}{2}$ and $(h, k) = (1, 3)$ .

– Write the equation

Put $m = - \frac{1}{2}$ and $(h, k) = (1, 3)$ in $y - k = m (x - h)$ to get,

$y - 3 = - \frac{1}{2} (x - 1)$

$y - 3 = - \frac{1}{2} x + \frac{1}{2}$ (Distributive property)

$y - 3 + 3 = - \frac{1}{2} x + \frac{1}{2} + 3$ (Add 3 to both sides)

$y = - \frac{1}{2} x + \frac{7}{2}$ (Simplify)

So, the required equation of the straight line in slope-intercept form is $y = - \frac{1}{2} x + \frac{7}{2}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Write an equation in slope-intercept form for the line that satisfies each set of conditions.
Slope $- \frac{1}{2}$ , passes through $(1, 3)$

Short Answer

Step by step solution

– State the concept

– List the given data

– Write the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Applied Mathematics

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Write an equation in slope-intercept form for the line that satisfies each set of conditions.Slope -12, passes through 1,3

Short Answer

Step by step solution

– State the concept

– List the given data

– Write the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Applied Mathematics

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Write an equation in slope-intercept form for the line that satisfies each set of conditions.
Slope $- \frac{1}{2}$ , passes through $(1, 3)$