Please answer the question in the picture

A point can be defined by (x, y), where x and y are the horizontal distance and the vertical distance respectively from point (0,0) (called the origin).

There are 3 ways to define a line:

(1) The slope-intercept form

y = mx + b, in which m is the slope, b is the y-intercept, where the line crosses the vertical axis at (0, b). If values of m and b are given, you can substitute and write the equation right away.

The slope, m, is calculated by rise (vertical difference between 2 points on the line) divided by run (horizontal difference between the 2 points on the line)

Step-by-step explanation:

or example, if 2 points on the line are

(x1, y1) and (x2, y2)

Then slope = (y1– y2)/(x1 — x2)

If m > 0, then the line rises to the right.

If m = 0, then the line is horizontal.

If m < 0, then the line rises to the left.

If the line is in the form x = c, where c is a constant, then the line is vertical.

(2) Point slope form

m = (y — y1)/(x — x1), when (x1, y1) and m are given.

In other words,

m(x — x1) = y — y1

mx — m(x1) = y — y1

y = mx — m(x1) + (y1)

Note that b = -m(x1) + (y1)

(3) linear form

ax + by + c = 0, where a, b, and c are constants.

3 0

3 years ago

What are the slope and y - intercept of the equation 6x+3y=-12

sertanlavr [38]

Answer:

Slope= -2

y-intercept= -4

Step-by-step explanation:

To find the slope and y-intercept of a given equation, first rearrange the equation such that it is in the slope-intercept form. In the slope-intercept form, the coefficient of y is 1 and the rest are moved to the left hand side of the equation.

$\textcolor{steelblue}{\text{Slope-intercept form}}$

y= mx +c, where m is the slope and c is the y-intercept

Given equation: 6x +3y= -12

Let's leave the y term on the left of the equation and bring the rest to the right.

3y= -6x -12

To ensure that the coefficient of y is 1, divide both sides by 3.

y= -2x -4

The equation is now in the slope-intercept form.

The slope is the coefficient of x (the number that comes before x), thus the slope is -2. The y-intercept is -4.

4 0

2 years ago

This is Algebra 2. help fast!

WINSTONCH [101]

Find VA
simplify fraction
set deonmenator equal to zero
that value is VA
cannot cross VA

fidn HA
if the degree of the numerator is less than the degree of the denomenator, then the HA is y=0
if the degree is equal, then divide he leading coeficient of the numerator by the leading coeficient of the deonmenator

to find if the fn crosses the HA, set the HA equaal to the reduced fn and solve, if you get a false statement, then it does not cross

holes are found by where if you have the numberator and deonmentoar are the same degree and they have a factor of same multiplicity example
f(x)= $\frac{(x+2)(x-3)}{(x-3)(x-5)}$
there is a hole at x=3 and to find the y coordinate, subsitute x=3 into reduced fraction

so

14.
make one fraction
f(x)=(2x-1)/(x-1)
x and y intercept
xint is f(x)=0
xintercept= 1/2 (1/2,0)
y intercept is when x=0 so set x=0
-1/-1=1
yintercept is y=1 aka (0,1)

VA set denom to zeero
x-1=0
x=1
VA at x=1

HA degree is same so divide leading coefs
2/1=2
HA at y=2

crosses HA?
2=(2x-1)/(x-1)
2x-1=x-1
x-1=-1
x=0
crosses ha at x=0 and
f(x)=(2(0)-1)/(0-1)=-1/-1=1
crosses HA at (0,1)

no holes

find where the fn is negative and positive
(2x-1) is zero at x=1/2
x-1 is zero at x=1
so in between, those, (1/2 and 1), the graph is negative (positive/negative=negative)
outside of that interval, the graph is positive (positive/positive=positive, negative/negative=negative) so graph is drawn on attachment

15. factor
f(x)=(x-2)/[(x-4)(x+1)]
VA set denom to zero
x-4=0
x+1=0
VAs at x=4 and -1

HA
degree of numberateor is smaller to HA is y=0

crosses HA?
0=(x-2)/(x^2-3x-4)
0=x-2
2=x
yes, at (2,0)

holes? no

find positive and negative

graph included

16.
VA=x is x=1
x=1
x-1=0
reduced denom is (x-1)
HA is y=2
degrees are same
2/1=2
(2x+something)/(x-1)
xint at -4,=
deonm when set to zero, etuals -4
2x+something=0 yeilds x=-4 so
2(-4)+something=0
-8+something=0
something=8

(2x+8)/(x-1)

hole at (6,4)
factored out bit is x=6
x=6
x-6=0

multiply whole equation by (x-6)/(x-6)

the function is
f(x)= $\frac{(2x+8)(x-6)}{(x-1)(x-6)}$ aka
f(x)= $\frac{2x^2-4x-48}{x^2-7x+6}$

17.
factor
f(x)= $\frac{(x+1)(x+5)}{(x-2)(x+5)}$
x+5=0
x=-5
hole at x=-5
sub into reduced fn (f(x)= $\frac{x+1}{x-2}$ )
4/7
hole at (-5,4/7)

degree is same so divide leading coeficients
1/1=1
HA=1

VA is set reduced denom to zero
(x-2) is reduced
x-2=0
x=2
VA is at x=2

6 0

3 years ago