Find the equation of a line which passes through point (-2, 3)?

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Find the equation of a line which passes through point (-2, 3) and is parallel to the line formed by the equation y = 4x + 7. Express it in slope-intercept form. Find the equation ...show more
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The slope intercept form is

y = mx + c

where m represents the slope (how much y increases, when x grows by 1), and
c is the intercept (the value of y when x=0)

If you have the slope of a line, then any parallel lines will have the same slope.
Any perpendicular line will have a slope of -1/m

Once you have the slope, you then find the intercept by fitting the point on the line.

Example, using number 1.

"parallel to the line y = 4x + 7"
this means that the slope of the new line will also be 4

y = 4x + c

Next, to find the intercept (c), we fit the point given: (x, y) = (-2, 3)
Points are always given in the form (x, y)
So, use the values for the variables:

y = 4x + c
becomes
3 = 4(-2) + c
3 = -8 + c
this forces us to use c = 11

the final answer:

y = 4x + 11

This line is parallel to the line y = 4x + 7 (it has the same slope) and it contains the point (-2, 3) because when you put these values for x and y, the equation is true.

3 = 4(-2) + 11
3 = -8 + 11
3 = 3
Yep, it is true.


---

For the last one (the perpendicular line), don't forget to change the slope to -1/m

The line given is y = 2x + 6
It has a slope of 2
A perpendicular line would have a slope of -1/2

y = (-1/2)x + c
we need to fit the point (x, y) = (-4, 15)
15 = (-1/2)(-4) + c
15 = 2 + c
13 = c

final answer:
y = (-1/2)x + 13
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  • girl next door answered 4 years ago
    I can help you do the first one , the others are quite similar
    use this form y=ax+b and we have a point x=-2 and y=3 and we also know that it's parallel to y=4x+7 so these two lines have the same slope which is 4

    then you simply solve the equation and find the b (y intercept)
    3=4*(-2)+b ==> b=11
    the line wanted is y=4x+11
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  • MegaMaster answered 4 years ago
    Parallel=Same Slopes//Perpendicular=Reciprocal Slopes

    1.y-y1=m(x-x1)
    y-3=4(x+2)
    y-3=4x+8
    y=4x+5

    2.y-y1=m(x-x1)
    y+5=3(x-4)
    y+5=3x-12
    y=3x-17

    3.y-y1=m(x-x1)
    y-5=3(x+4)
    y-5=3x+12
    y=3x+17

    4.y-y1=m(x-x1) slope=1/2=-.5
    y-15=-.5(x+4)
    y-15=-.5x-2
    y=-.5x+13

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