MATHEMATICS HIGH SCHOOL

What is the equation in slope-intercept form of the line that passes through the points ( -4 , 2) and (12, 6)?Group of answer choices

y = 0.25x − 4.5

y = 4x − 42

y = 4x + 18

y = 0.25x + 3

Answers

Answer 1

Answer:

Answer:

y = 0.25x + 3

Step-by-step explanation:

solve for slope:

(6-2)/(12+4) = 1/4

solve for b:

6 = 12(1/4) + b

6 = 3 + b

b = 3

equation can also be y = 1/4x + 3

Answer 2

Answer:

Step-by-step explanation:

let the equation be y = mx + b.

m = (6 - 2)/(12 - (-4)) = 1/4

sub (12, 6):

6 = 1/4(12) + b

b = 3

therefore, equation of the line is y = 1/4x + 3, aka option 4

Topic: coordinate geometry

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Related Questions

Complete the statements below about the graphs of y=-2x and y=x
Which equation represents the line that passes through the point (1, 5) and has a slope of -2?
9/10( -2/3) ( symplify )
Find the distance between (-6,8) and (10,-4)
Given the equations y = x2 - 4x - 5 and y + x = -1, one point that satisfies both equations is

On earth, a kilogram is equivalent to 2.2 pounds.

[True]
or
[False]

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False one pound is equal to less than one kilo

Answer:

false

Step-by-step explanation:

because I say

Which whole number property was used?23 + 2 = 2 + 23
Commutative Property of Addition
Associative Property of Addition
Identity Property of Addition

Answers

Answer:

Commutative property of addition is the correct option.

Answer:

the answer commutative my friend

I am about to fail this math class. I would like to verify that my answers are right. Please help.Find the distance from the given point to the vertical axis.
(7, −6)

Determine the value of k such that the points whose coordinates are given lie on the same line.
(k, 0), (0, −1), (10, −11)

Find the slope of the line containing the given points.
P1(5, −9), P2(1, 7)

Find the equation of the line that passes through the midpoint of the line segment between
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Let y be the dependent variable and let x be the independent variable.

Find the equation of the line that contains the given point and has the given slope.
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Suppose a ball is being twirled at the end of a string and the center of rotation is the origin of a coordinate system. If the string breaks, the initial path of the ball is on a line that is perpendicular to the radius of the circle. Suppose the string breaks when the ball is at the point whose coordinates are P(3, 9). Find the equation of the line on which the initial path lies

During one month, a homeowner used 500 units of electricity and 100 units of gas for a total cost of $331. The next month, 400 units of electricity and 250 units of gas were used for a total cost of $326. Find the cost per unit of gas.

Answers

Answer:

1) 7 2) (-1,0) 3) m=-4 4) y=3x-4 5) y=x+6 6)

g(x)=-1/3x+10 7) y= $0.36

Step-by-step explanation:

These questions are all about Cartesian Geometry.

1) The Distance from point (7,-6) to vertical axis (0,-6) is measured with a straight line, between point (7,-6) and nearer point (0,-6)

d=|7-0|=7

2) To determine the value of k, let's determine the function with the two known points: (0, −1), (10, −11).

$m=(y_(2)-y_(1))/(x_(2)-x_(1))\Rightarrow m=(-11+1)/(10-0)\Rightarrow m=-1\n-11=-1*(10)+b\therefore b=-1\Rightarrow f(x)=-x-1\nf(k)=-k-1\n0=-k-1\therefore k=-1$

So (k,0)=(-1,0)

3) To find the slope of the line, we must apply that formula used above.

$m=(y_(2)-y_(1))/(x_(2)-x_(1))\Rightarrow m=(7+9)/(1-5)\Rightarrow m=(16)/(4)=-4$

4) To find the equation of the line which the midpoint (2,2) since Midpoint is given by

$Midpoint=((x_(1)+x_(2))/(2)+(y_(1)+y_(2))/(2))\n$

And the slope is 3, then m=3. Notice the formula is the same to calculate the slope, but we will only pick one point. Since (2,2) ∈ to the function let's use this point, as initial value (x0,y,0)

$m(x-x_(0))=y-y_(0)\n3(x-2)=y-2\n3x-6=y-2\Rightarrow 3x-y=6-2\Rightarrow -y=4-3x\Rightarrow y=3x-4$

5) Similarly to the previous one:

$m(x-x_(0))=y-y_(0)\n(x-0)=y-6\nx=y-6\Rightarrow -y=-x-6\Rightarrow y=x+6$

6) A ball being twirled. The center of the rotation is the origin of Coordinate System (0,0) when the string breaks at point (3,9)

If the line was straight from the origin to point (3,9) $m=(9-0)/(3-0)\Rightarrow m=3\therefore 9=3(3)+b\Rightarrow b=0\Rightarrow f(x)=3x$

But the point (3,9) ∈ to a tangent line to the circumference described by the twirling.

Since it is perpendicular instead of m=3 it is -1/m i.e. -1/3, also the circumference intercepts the y-axis in ≈10

g(x)=-1/3x+10

7) In this case, we must also find the function.

x=units of electricity, y=units of gas |

500x+100y=331

400x+250y=326

The cost per unit of gas is y. Finding out the unit value for y

$100y=331-500x\rightarrow y=(331-500x)/(100)\n500x=331-100y\nx=(331-100y)/(500)\n400((331-100y)/(500))+250y=326\n52.96-80y+250y=326\Rightarrow y=(9)/(25) \,and \,x=(59)/(100)$

Write the equation of the line that passes through (−3, 5) and (2, 10) in slope-intercept form.y = x + 8
y = x − 8
y = −5x − 10
y = −5x + 20

Answers

m = (y2 -y1)/(x2-x1)
m = (10 -5 )/(2+3)
m = 5 / 5
m = 1

using y = mx + b passing through (−3, 5)
5 = 1(-3) + b
5 + 3 = b
so b = 8

equation

y = x + 8

answer: y = x + 8 (first choice)

first you have to find the slope by doing y2-y1 / x2-x2 which will be 10-5 over 2-(-3)

Simplify and you get 5/5 which is one

Now solve for d by plugging a set of points back in and you get 8=d

so y=x+8

What are the real imaginary solutions of the polynomial equation?
x^3=216

Answers

When you look at it, you would wonder why this equation is considered to be a polynomial where in fact there is only one factor. The only reason to explain this is that the other factors have zero as the coefficient. On another note, to answer this problem, we need to get the cube root of 216 which is 6, which is also the answer to this problem.

At lunch, Kira eats either a burrito containing 490 milligrams of sodium or a peanut butter sandwich containing 700 milligrams of sodium. Her doctor told her to reduce her sodium to no more than 4,000 milligrams per week. Which inequality represents x, the number of microwave burritos, and y, the number of peanut butter sandwiches, she can eat each week?
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Answers

If
x is the number of microwave burritos
y is the number of peanut butter sandwiches
4000 is the maximum allowable sodium intake

Then, the inequality is:
490x + 700 y ≤ 4000

The correct answer is the second option.

Answer:

answer is b

Step-by-step explanation:

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