Algebra I
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Write an equation in slope-intercept form for the line that passes through and that is perpendicular to a line which passes through the two points
and
.
Explanation
Find the slope of the line through the two points. It is .
Since the slope of a perpendicular line is the negative reciprocal of the original line, the new line's slope is . Plug the slope and one of the points into the point-slope formula
. Isolate for
.
Write an equation in slope-intercept form for the line that passes through and that is perpendicular to a line which passes through the two points
and
.
Explanation
Find the slope of the line through the two points. It is .
Since the slope of a perpendicular line is the negative reciprocal of the original line, the new line's slope is . Plug the slope and one of the points into the point-slope formula
. Isolate for
.
What line is perpendicular to through
?
Explanation
Perdendicular lines have slopes that are opposite reciprocals. The slope of the old line is , so the new slope is
.
Plug the new slope and the given point into the slope intercept equation to calculate the intercept:
or
, so
.
Thus , or
.
Write an equation in slope-intercept form for the line that passes through and that is perpendicular to a line which passes through the two points
and
.
Explanation
Find the slope of the line through the two points. It is .
Since the slope of a perpendicular line is the negative reciprocal of the original line, the new line's slope is . Plug the slope and one of the points into the point-slope formula
. Isolate for
.
What line is perpendicular to through
?
Explanation
Perdendicular lines have slopes that are opposite reciprocals. The slope of the old line is , so the new slope is
.
Plug the new slope and the given point into the slope intercept equation to calculate the intercept:
or
, so
.
Thus , or
.
What line is perpendicular to through
?
Explanation
Perdendicular lines have slopes that are opposite reciprocals. The slope of the old line is , so the new slope is
.
Plug the new slope and the given point into the slope intercept equation to calculate the intercept:
or
, so
.
Thus , or
.
A straight line passes through the points and
.
What is the -intercept of this line?
Explanation
First calculate the slope:
The standard equation for a line is .
In this equation, is the slope of the line, and
is the
-intercept. All points on the line must fit this equation. Plug in either point (1,3) or (2,2).
Plugging in (1,3) we get .
Therefore, .
Our equation for the line is now:
To find the -intercept, we plug in
:
Thus, the -intercept the point (4,0).
What line is perpendicular to through
?
Explanation
Perdendicular lines have slopes that are opposite reciprocals. The slope of the old line is , so the new slope is
.
Plug the new slope and the given point into the slope intercept equation to calculate the intercept:
or
, so
.
Thus , or
.
A straight line passes through the points and
.
What is the -intercept of this line?
Explanation
First calculate the slope:
The standard equation for a line is .
In this equation, is the slope of the line, and
is the
-intercept. All points on the line must fit this equation. Plug in either point (1,3) or (2,2).
Plugging in (1,3) we get .
Therefore, .
Our equation for the line is now:
To find the -intercept, we plug in
:
Thus, the -intercept the point (4,0).
A straight line passes through the points and
.
What is the -intercept of this line?
Explanation
First calculate the slope:
The standard equation for a line is .
In this equation, is the slope of the line, and
is the
-intercept. All points on the line must fit this equation. Plug in either point (1,3) or (2,2).
Plugging in (1,3) we get .
Therefore, .
Our equation for the line is now:
To find the -intercept, we plug in
:
Thus, the -intercept the point (4,0).