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Geometry/Geometry: Lines in the coordinate plane


QUESTION: Okay so, I don't understand this question or what it wants me to do...
The directions say Write the slope-intercept formand point-slope form of the equation of the line described, the question says: through: (2,5), parallel to y=(7/2)x+3

ANSWER: The slope-intercept form of a line is y = mx + b.
That is because m is the slope and b is the y intercept.

Since we are given it is parallel to y = (7/2)x + 3,
and the slope of that line is 7/2, that is the slope to use.

We are given it goes through the point (2,5),
so start with the point-slope form.
That is, y - y0 = m(x-x0) where x0 = 2, y0 = 5, and m = 7/2.

That gives y - 5 = (7/2)(x-2).

This can be converted to the slope-intercept form by multiplying it out
and rearranging some terms.

It becomes, after multiplying it out, y - 5 = (7/2)x - 7.

We still have a -5 on the left that doesn't go there, so add 5 to both sides.
This gives y = (7/2)x - 2.

---------- FOLLOW-UP ----------

QUESTION: Thank you, what do you do when it asks...
Through: (1, 5), parallel to y=-5x

Use the point-slope form of a line.
That is, y-y1 = m(x-x1) where (x1,y1) is the point and m is the slope.

We are given (x1,y1) = (1,5).

The standard line is y = mx + b, and we have y = -5x, so b=0 and m=-5.

So, just take x1=1, y1=5, and m=-5 and put them in the equation of the line given at first.
That is, y-y1 = m(x-x1).  This gives y-5 = -5(x-1).

This can be multiplied out to give y-5 = -5x + 5.
Moving the -5 to the right so we have an equation for y is the same as adding 5 to both sides.
This gives y = -5x + 10.


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Scott A Wilson


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