# 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.
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Best Answer

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

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

### Other Answers (2)

Rated Highest-
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 -
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### Source(s):

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