The equation of the line that passes through the point ( 2 , − 5 ) .

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter T, Problem 1BDT

(a)

To determine

To find: The equation of the line that passes through the point (2,−5).

Expert Solution

The equation of the line is y=3x+1.

Explanation of Solution

Given:

The slope of the line is 3.

Formula used:

The equation of the straight line is y=mx+c, where m is the slope of the line, c is the x-intercept.

Calculation:

Suppose, the equation of the straight line is y=mx+c.

It is given that, the slope of the line is 3.

Thus, substitute m=3 in y=mx+c to obtain the equation of the straight line,

y=3x+c

It is given that, the line passes through the point (2,5).

Thus, substitute x=2 and y=5 in y=3x+c to obtain the equation of the straight line,

5=3×2+cc=5+6c=1

Thus, substitute c=1 in y=3x+c to obtain the equation of the straight line,

y=3x+1

Thus, the equation of the line is y=3x+1.

(b)

To determine

To find: The equation of the line that passes through the point (2,−5).

Expert Solution

The equation of the line is y=5.

Explanation of Solution

Given:

The line is parallel to the x-axis.

Formula used:

The equation of the straight line that is parallel to the x-axis is y=a, where a is a constant.

Calculation:

It is given that the line is parallel to the x-axis.

Suppose, the equation of the straight line is y=a.

It is given that, the line passes through the point (2,5).

Thus, substitute x=2 and y=5 in y=a to obtain the equation of the straight line,

y=5

Thus, the equation of the line is y=5.

(c)

To determine

To find: The equation of the line that passes through the point (2,−5).

Expert Solution

The equation of the line is x=2.

Explanation of Solution

Given:

The line is parallel to the y-axis.

Formula used:

The equation of the straight line that is parallel to the y-axis is x=a, where a is a constant.

Calculation:

It is given that the line is parallel to the y-axis.

Suppose, the equation of the straight line is x=a.

It is given that, the line passes through the point (2,5).

Thus, substitute x=2 and y=5 in x=a to obtain the equation of the straight line,

x=2

Thus, the equation of the line is x=2.

(d)

To determine

To find: The equation of the line that passes through the point (2,−5).

Expert Solution

The equation of the line is y=12x6.

Explanation of Solution

Given:

The line is parallel to the line 2x4y=3.

Formula used:

The equation of the straight line is y=mx+c, where m is the slope of the line, c is the x-intercept.

Calculation:

Suppose, the equation of the straight line is y=mx+c.

It is given that, the line is parallel to the line 2x4y=3, that is y=12x34.

The slope of the line 2x4y=3 is 12.

Thus, substitute m=12 in y=mx+c to obtain the equation of the straight line,

y=12x+c

It is given that, the line passes through the point (2,5).

Thus, substitute x=2 and y=5 in y=12x+c to obtain the equation of the straight line,

5=12×2+cc=51c=6

Thus, substitute c=6 in y=12x+c to obtain the equation of the straight line,

y=12x6

Thus, the equation of the line is y=12x6.

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