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Mrrafil [7]
3 years ago
6

How do you solve the three forms: Slope Y-intercept form Standard Form Point slope form

Mathematics
1 answer:
Nostrana [21]3 years ago
4 0

Answer:An equation in the slope-intercept form is written as

y=mx+b

Where m is the slope of the line and b is the y-intercept. You can use this equation to write an equation if you know the slope and the y-intercept.

Example

Find the equation of the line

Choose two points that are on the line

Calculate the slope between the two points

m=y2−y1x2−x1=(−1)−33−(−3)=−46=−23

We can find the b-value, the y-intercept, by looking at the graph

picture28

b = 1

We've got a value for m and a value for b. This gives us the linear function

y=−23x+1

In many cases the value of b is not as easily read. In those cases, or if you're uncertain whether the line actually crosses the y-axis in this particular point you can calculate b by solving the equation for b and then substituting x and y with one of your two points.

We can use the example above to illustrate this. We've got the two points (-3, 3) and (3, -1). From these two points we calculated the slope

m=−23

This gives us the equation

y=−23x+b

From this we can solve the equation for b

b=y+23x

And if we put in the values from our first point (-3, 3) we get

b=3+23⋅(−3)=3+(−2)=1

If we put in this value for b in the equation we get

y=−23x+1

which is the same equation as we got when we read the y-intercept from the graph.

To summarize how to write a linear equation using the slope-interception form you

Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.

Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

Once you've got both m and b you can just put them in the equation at their respective position.

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Select the descriptions that are true of the equation y - 6= - 3(x+2). Select all that apply.
Lapatulllka [165]

The point-slope form:

y-y_1=m(x-x_1)

We have

y-6=-3(x+2)\to y-6=-3(x-(-2))

Therefore

<h3>slope = -3 and the point (-2, 6)</h3>

------------

<h3>y + 2 = 2(x - 1)</h3>

2x - y = 4    <em>it's standard form Ax + By = C</em>

y = 2x - 4     <em>it's slope-intercept form y = mx + b</em>

y - x = 4 →<em> </em>x - y = -4  <em>t's standard form Ax + By = C</em>

3 0
3 years ago
Evaulate<br> -7(5+3)-|-6|
s2008m [1.1K]
-7(8)-|-6|
-56-6 = -62
7 0
3 years ago
Read 2 more answers
Can I get some help?​
ruslelena [56]

Answer:

y = 4x - 9

Step-by-step explanation:

The points on the graph we can see clearly are (1, -5) and (2, -1).

The equation of the line is in the form <u>slope-intercept</u>, where the general formula is y = mx + b.

We need to find "m", the slope of the line; and "b", the y-intercept.

Use the two points we found in the formula for calculating slope m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}.

Choose which is point 1 and point 2:

Point 1 (1, -5)    x₁ = 1   y₁ = -5

Point 2 (2, -1)   x₂ = 2  y₂ = -1

Substitute x₁, x₂, y₁, and y₂

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

m=\frac{-1-(-5)}{2-1}       Solve in the numerator and denominator

m=\frac{4}{1}        Simplify the fraction

m=4           Slope of the line

Find "b":

Substitute a point's "x" and "y" coordinates, and the slope, "m", into the general formula for slope-intercept.

I will use point 2:

x = 2; y = -1; m = 4

y = mx + b

-1 = (4)(2) + b         Multiply

-1 = 8 + b            Start isolating "b"

-1 - 8 = 8 - 8 + b            Subtract 8 from both sides

-1 - 8 = b           "b" is isolated

b = -9           Answer for "b", y-intercept.

The variable should be on the left side for standard formatting.

Take the general formula: y = mx + b

Replace "m" and "b" with the values we found.

y = 4x - 9

8 0
3 years ago
The balance in Beth's checking account is $75. She must deposit enough money in her account to be able to pay the electric bill,
Evgen [1.6K]
75+d=110  subtract 75 from both sides

d=$35

So she needs to deposit at least $35 to be able to pay the electric bill.
5 0
3 years ago
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Answer for x.<br><br> 1. 3x - 10 = -21<br><br> 2. -22 - 4x = 12
ra1l [238]

Answer:

3x - 10 = -21

add 10 on both side

3x-10+10=-21+10

3x=-11

divide both side by 3

3x/3=-11/3

x=-11/3

Step-by-step explanation:

2. -22 - 4x = 12

add 22 on both side

-22+22-4x=12+22

-4x=36

divide both side by -4

-4x/-4=36/-4

c=-9 is your answer

4 0
3 years ago
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