Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the given equation.

(0,3),y=3x+5

Short Answer

Expert verified

The required equation of the line in slope-intercept form isy=3x+3

Step by step solution

01

Step 1. Slope-intercept form of an equation of a line:

The slope-intercept form of an equation of a line is given by

y=mx+b.........1

Where , slope =m, and, y-axis intercept=b.

02

Step 2. Write an equation of a line passing through a point (x1,y1) and having slope m.

The equation of a line passing through a pointx1,y1 and having slopem is given byrole="math" localid="1647430983632" yy1=mxx1..........2

03

Step 3. Write the equation of the line that passes through the point (2,5) and is parallel to the line y=x−3. 

The equation of the given line is,

y=3x+5........3

Compare (3) with (1).

The slope of the line 3=3

Since, the unknown line is parallel to the line (3).

Since, two lines are parallel to each other if the slope of one of the line is equal to the slope of the other line.

So, the slope of the unknown line (m)=the slope of the line (3) =3

Since, the unknown line passes through the point 0,3

Therefore, substitute x1=0,y1=3and m=3, in (2)

y3=3x0y3=3xy=3x+3

This is the equation of the unknown line in slope-intercept form y=mx+b, where m=3and b=3.

Therefore the required equation of the line in slope-intercept form is y=3x+3.

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.

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

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Study anywhere. Anytime. Across all devices.

Sign-up for free