Solve Slope Intercept Equations: (2,1), 4x-2y=3

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In summary, the conversation discussed finding the slope-intercept forms of equations for lines passing through a given point and either parallel or perpendicular to a given line. The attempt at solving the problem involved using the point-slope formula and the slope-intercept formula, but resulted in incorrect answers. It was suggested to use the slope-intercept formula in conjunction with the knowledge that parallel lines have the same slope and perpendicular lines have a negative reciprocal slope, which would yield the correct answers. The conversation ended with the suggestion that this method may be quicker and easier than using the point-slope formula.
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mistalopez
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Homework Statement



Write the slope intercept forms of the equation of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.

Point: (2,1) Line: 4x-2y=3

Homework Equations



y-y1=m(x-x1)

y=mx+b

The Attempt at a Solution



I first put the line into slope intercept form: y=-2x+(3/2)

a) Next, I used point-slope to get the parallel line:
y-y1=m(x-x1)
y-1=-2(x-2)
y-1=-2x+4
y=-2x+5
*However, the correct answer should be y=2x-3

b) I used the reciprical of the slope to make it perpendicular: m = 1/2
Next I used the point-slope to find the perpendicular line of the equation.
y-y1=m(x-x1)
y-1=(1/2)(x-2)
y-1=(1/2x)-1 *Multiply both sides by 2 to remove fraction
2(y-1)=((1/2x)-1)2
2y-2=1x-2
2y=1x
y=1x/2
*However, the correct answer in the book is y=(-1/2x)+2

What am I doing wrong?
 
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  • #2
I first put the line into slope intercept form: y=-2x+(3/2)


it should be y = 2x - 3/2, you'll probably get the right answer with that
 
  • #3
Conveniently, one doesn't even have to use the point slope formula to solve this problem. By simply knowing that parallel lines have the same slope and perpendicular lines have a negative reciprocal slope and using the slope-intercept equation will yield you the proper result. For instance:

The slope intercept form of 4x - 2y = 3 would be:

y = 2x - [tex]3/2[/tex]

For the parallel line, one would know that the slope must be the same as the given, thus, in this case, the slope would be 2. By using the given points, (2,1), one can determine the y-intercept of the parallel line like so:

1 = 2(2) + b

and solve for b.

The equation for the parallel line would then be y = 2x + whatever b would be.

The perpendicular line's equation is determined just the same. By knowing that the slope of a line perpendicular to the given is a negative reciprocal, one will see that the slope in this case would be [tex]-1/2[/tex] and thus:

1 = [tex]-1/2[/tex](2) + b

and solve for b once more.

I've always found this method quicker and easier for me than using the point-slope equation. Hopefully it will help you.
 

1. What is a slope intercept equation?

A slope intercept equation is a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept. This form makes it easy to graph the equation and determine the slope and y-intercept.

2. How do I solve a slope intercept equation?

To solve a slope intercept equation, you can use the given point and the slope to find the y-intercept. Plug in the values of x and y from the given point into the equation, and then solve for b. Once you have the value of b, you can write the equation in y = mx + b form.

3. What is the point-slope form of a linear equation?

The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. This form is useful for finding the equation of a line when given a point and the slope.

4. How can I check my answer for a slope intercept equation?

To check your answer for a slope intercept equation, you can substitute the x and y values from the given point into the equation. If the equation holds true, then you have solved the equation correctly.

5. Can a slope intercept equation have a negative slope?

Yes, a slope intercept equation can have a negative slope. The slope is simply a measure of how steep the line is, and it can be positive or negative depending on the direction of the line.

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