Slope-intercept trouble?

Question

Can't figure out the slope-intercept form of the equation for the lines that pass through these points...

(0, -1) has slope -2

(0, 3) has slope 3/2

(-4, -5) has -8

(10, 6) has slope 4/3

...and the slope-intercept form that passes through these points...

(-7, -1) and (-9, 4)

Answer 1

slope intercept form : y=mx+b where y is the y coordinate, x is the x coordinate m is the slope and b is the y-intercept

i will do the first one for you, you should be able to follow the rest

(0,-1) slope -2
x=0 y=-1 m=2 plug these into the slope intercept equtaion
-1=(-2)(0)+y solve for y and get y=-1
therefore the slope intercept equation for the first one would be y=-2x+(-1) or y=-2x-1

for the last one you will need to find the slope of the line using the formula m = y2-y1/x2-x1 and then follow the steps

Answer 2

When a point (x1,y1) and slope m are given , the equation of line in point slope form is

y-y1 = m(x-x1)

1)

here x1 = 0, y1 = -1 and slope m = -2

the equation is

y -(-1) = -2(x - 0)

y + 1 = -2x

y = -2x - 1

2)

here x1 = 0, y1 = 3 and m =3/2

y-3 = (3/2)(x-0)

y - 3 = (3/2)x

multiply with 2

2y - 6 = 3x

2y = 3x + 6

3)

x1 = -4, y1 = -5 and m =-8

y +5 = -8(x + 4)

y + 5 = -8x - 32

y = -8x - 37

4)

x1 = 10, y1 = 6 , m = 4/3

y - 6 = (4/3)(x - 10)

multiply with 3

3y - 18 = 4x - 40

3y = 4x - 22

5)

Here slope is not given. But coordinates of two points are given.
First find out the slope using m =(y2-y1)/(x2-x1)

x1= -7, y1 = -1

x2 = -9, y2 = 4

slope, m = (y2-y1)/(x2-x1)

m = [4 -(-1)]/[(-9 -(-7)] = 5/-2 = -5/2

to get the equation of the line with slope, -5/2 use any one of the given points , either(-7, -1) or (-9 , 4) in point slope form.

y - 4 = (-5/2)(x +9)

multiply with 2

2y - 8 = -5x - 45

2y = -5x - 37

Answer 3

memorize;
y=m(x-h) + k
(h,k) are the coordinates of a point on a line m is the slope
1)
y = -2(x-0) -1
y= -2x -1

problem 2-3 are the same.
4)
y = 4/3(x-10) +6
y = 4/3*x -40/3 +18/3
y = 4/3*x - 22/3

5) first find the slope then use either point for (h,k) It doesn't matter which point you choose the results will be the same.
m = (4-(-1))/(-9-(-7)) = 5/-2
You canfinish the problem.
Good luck!

Answer 4

(0, -1) has slope -2
y = -2x+b , so -1 = b, so y= -2x-1

(0, 3) has slope 3/2
y= 3x/2 +b, so 3= b, so y = 3x/2 +3
(-4, -5) has -8

(10, 6) has slope 4/3
y=4x/3+b, so 6 = 40/3 +b, so b= -22/3, so y =4x/3-22/3

(-7, -1) and (-9, 4)
slope = (4-(-1))/(-9 -(-7)) = 5/-2 = -5/2
Y = -5x/2 + b , so 4 = -5(-9)/2 +b, so b = 4 +45/2 = 26.5
so y = -5x/2 +26.5

Answer 5

for a equation of a line using slope & 1 point on the line, the formula is

m=(y-y1)/(x-x1)

1)(0, -1) has slope -2
m=-2 & (x1,y1)=(0,-1)
so apply the formula
m=(y-y1)/(x-x1)
-2=(y-{-2})/(x-0)
-2=(y+2)/(x)
-2x=(y+2)
-2x=y+2
-2x-2=y

2)(0, 3) has slope 3/2
m=3/2 & (x1,y1)=(0,-3)
so apply the formula
m=(y-y1)/(x-x1)
3/2=(y-3)/(x-0)
3/2=(y-3)/(x)
3/2(x)=(y-3)
3(x)=(y-3)(2)
3x=2y-6
3x+6=2y


3)(-4, -5) has -8
m=-8 & (x1,y1)=(-4,-5)
so apply the formula
m=(y-y1)/(x-x1)
-8=(y-{-5})/(x-{-4})
-8=(y+5)/(x+4)
-8(x+4)=(y+5)
-8x-32=y+5
-8x-32-5=y
-8x-37=y


4)(10, 6) has slope 4/3
m=4/3 & (x1,y1)=(10,6)
so apply the formula
m=(y-y1)/(x-x1)
4/3=(y-6)/(x-10)
4/3(x-10)=(y-6)
4(x-10)=3(y-6)
4x-40=3y-18
4x-40+18=3y
4x-22=3y

5) when u have 2 points through which the line passes, then the equation of the line is
(y-y1)/(x-x1)=(y2-y1)/(x2-x1)
(x1,y1)=(-7,-1) & (x2,y2)=(-9,4)

now substitute this in the formula
(y-{-1})/(x-{-7})=(4-{-7})/({-9}-{-7})
(y+1)/(x+7)=(4+7)/(-9+7)
(y+1)/(x+7)=(11)/(-2)
(y+1)(-2)=(11)(x+7)
-2y-2=11x+77
-2y=11x+77+2
-2y=11x+79
2y=-11x-79

Answer 6

y=mx+b
x=0, y=-1, m=-2
-1=-2*0+b
b=-1
y=-2x-1


y=mx+b
x=-4, y=-5, m=-8
-5=-8*-4+b
b=-37
y=-8x-37

on the last one find m (slope)
m=(-1-4)/(-7--9)=-5/2
x=-7 y=-1
-1=(-5/2)*-7+b
-1=35/2+b
b=-37/2
y=(-5/2)x-(37/2)