equations of lines, math homework help

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algrnpue

Mathematics

Description

Write the equation of a line in point-­slope form with a slope of bevelled 1 half containing the point (-3, 1)


y + 1 = (bevelled 1 half)(x - 3)

y - 1 = (bevelled 1 half)(x + 3)

y + 3 = (bevelled 1 half)(x - 1)

y - 3 = (bevelled 1 half)(x + 1)

======================

Write the equation of a line in slope-­intercept form with a slope of -2 containing the point (1, 3).


y = -2x + 5

y = -2x - 5

y = -2x + 2

y = -2x + 7

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Write the equation of a line in slope-­intercept form that passes through the points (-2, 1) and (4, 4).


y = 2x - 4

y = (bevelled 1 half)x + 2

y = 2x + 5

y = (bevelled 1 half)x

================================

Write the equation of a line in standard form that passes through the points (8, 2) and (-2, -3).


minus 1 half x + y = -2

-x + 2y = -4

-2x + y = 1

-2x + y = -14

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Write the equation of a line in slope-­intercept form containing the point (5, 1) that is perpendicular to the line -5x + 4y = -2.


y equals minus 4 over 5 x space plus space 5

y equals minus 4 over 5 x space minus space 3

y equals minus 4 over 5 x space minus space 4

y equals 4 over 5 x minus 4

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The annual average income y of an American man with an associate’s degree is given by the linear equation y = 1983x + 42,972, where x is the number of years after 1999. What does the slope of the equation represent? (Source: Based on data from U.S. Bureau of the Census, 1999­-2004).


The average annual income of an American man with an associate’s degree in 1983.

The number of years since 1999 that the average man with an associate’s degree had income.

The increase in the average annual income of an American man with an associate’s degree each year.

The average annual income of an American man with an associate’s degree in 1999.

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The annual average income y of an American man with an associate’s degree is given by the linear equation y = 1983x + 42,972, where x is the number of years after 1999. What does the y-intercept of the equation represent? (Source: Based on data from U.S. Bureau of the Census, 1999-2004).


The average annual income of an American man with an associate’s degree in 1983.

The number of years since 1999 that the average man with an associate’s degree had income.

The increase in the average annual income of an American man with an associate’s degree each year.

The average annual income of an American man with an associate’s degree in 1999.

======================

Write the equation of a line in slope intercept form containing the point (-1, 8) that is parallel to the line 3x + y = -4.


y = 3x + 11

y = -3x + 5

y = -3x + 9

y = 3x + 9

==============================

Write the equation of a vertical line containing the point (1, 8)


x = 1

x = 8

y = 1

y = 8

=============================

Write the equation of a horizontal line containing the point (5, -3).


x = 5

x = -3

y = 5

y = -3

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Explanation & Answer

Attached are the solutions.Please let me know if you have any questions about these problems.

Equations of Lines

Write the equation of a line in point-slope form with a slope of
point (-3, 1)

containing the

Point slope form of a line is :
Y - y1 = m( x - x1 )
Where m = slope and (x1, y1) is a point on the line.
Y - 1 = 1/2 (x - -3)
Y - 1 = 1/2 ( x+ 3 )

y+1=(

)(x - 3)

y-1=(

)(x + 3)

y+3=(

)(x - 1)

y-3=(

)(x + 1)

======================
Write the equation of a line in slope-intercept form with a slope of -2 containing the
point (1, 3).
Slope intercept form is y = mx + b. However since we know the slope and a point,
begin by writing the line in point slope form and transforming the equation by solving
for y.
y - 3 = -2(x-1)
Y-3 = -2x + 2

Y = -2x + 5

y = -2x + 5

y = -2x - 5

y = -2x + 2

y = -2x + 7
========================================
Write the equation of a line in slope-intercept form that passes th...


Anonymous
Excellent resource! Really helped me get the gist of things.

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