Equation of a line, in general form, that is perpendicular to 2x-3y + 7 = 0 and passes through the point (-3/4, 1)
1 answer:
Answer:
12x +8y +1 = 0
Step-by-step explanation:
You can write the equation by swapping the x- and y-coefficients and negating one of them. Then compute the constant that makes the line go through the given point. You can do that like this:
3(x-(-3/4)) +2(y -1) = 0
3x +9/4 +2y -2 = 0 . . . . eliminate parentheses
3x +2y +1/4 = 0 . . . . . . . simplify
To eliminate the fraction, multiply by 4:
12x +8y +1 = 0
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<em>Comment on the equation</em>
The line ax+by=0 passes through the origin. Replacing x and y with x-h and y-k, respectively, makes the line pass through the point (h, k). That's what we did above to make the line pass through the given point.
The business of swapping coefficients and negating one causes the slope of the new line to be the negative reciprocal of the slope of the original line. That is what makes the new line perpendicular to the original.
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Answer:
.
Step-by-step explanation:
On a cartesian plane, the -intercept of a function is the point where the graph of that function intersects with the
-axis.
The -axis of a cartesian plane is the same as the equation
(that is, the collection of all points with an
-coordinate of
.)
Construct a system of two equations, with one equation representing -axis and
to represent the graph of this function:
.
Solve this system for and for
. If a solution exists, then the
-axis and the graph of
would indeed intersect. The point
would be the intersection of the
-axis and the graph of
.
Substitute the second equation of the system into the first.
.
Hence, the intersection of the -axis and the graph of
would be
. By definition, this point would be the
-intercept of
.