The point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = (x – 12). What is the standard form of the equation for this line?

Answers

Answer 1

Answer:

The equation of line passes through points $\left({ - \,4, - \,3}\right)$ and $\left({12,1}\right)$ in standard form is $\boxed{{\mathbf{x - 4y = 8 }}}$ .

Further explanation:

It is given that a line passes through points $\left({ - 4, - 3}\right)$ and $\left({12,1}\right)$ .

The slope of a line passes through points $\left({{x_1},{y_1}}\right)$ and $\left({{x_2},{y_2}}\right)$ is calculated as follows:

$m=\frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}{\text{ }}$ ......(1)

Here, the slope of a line is denoted as and points are $\left({{x_1},{y_1}}\right)$ and $\left({{x_2},{y_2}}\right)$ .

Substitute for ${x_1}$ , $-3$ for ${y_1}$ , $12$ for ${x_2}$ and $1$ for ${y_2}$ in equation (1) to obtain the slope of a line that passes through points $\left({ - 4, - 3}\right)$ and $\left({12,1}\right)$ .

$\begin{aligned}m&=\frac{{1 - \left({ - 3}\right)}}{{12 - \left({ - 4}\right)}}\n&=\frac{{1 + 3}}{{12 + 4}}\n&=\frac{4}{{16}}\n&=(1)/(4)\n\end{aligned}$

Therefore, the slope is $(1)/(4)$ .

The point-slope form of the equation of a line with slope $m$ passes through point $\left({{x_1},{y_1}}\right)$ is represented as follows:

$y - {y_1}=m\left({x - {x_1}}\right){\text{}}$ ......(2)

Substitute for ${x_1}$ , $1$ for ${y_1}$ and $(1)/(4)$ for $m$ in equation (2) to obtain the equation of line.

$\begin{aligned}y - 1&=(1)/(4)\left({x - 12}\right)\n4\left({y - 1}\right)&=x - 12\n4y - 4&=x - 12\nx - 4y&=8\n\end{aligned}$

Therefore the standard equation of line that passes through points $\left({ - 4, - 3}\right)$ and $\left({12,1}\right)$ is $x - 4y = 8$ .

Thus, theequation of line passes through points $\left({ - 4, - 3}\right)$ and $\left({12,1}\right)$ in standard form is $\boxed{{\mathbf{x - 4y = 8 }}}$

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Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Coordinate Geometry

Keywords:Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics,equation of line, line, passes through point

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I need help with this math question on my study guide!Sadly, I do not remember how to do this and I would greatly appreciate any help you can offer.

Answers

Sadly is right. You must have practiced this stuff in middle school
until it was coming out of your ears. Fortunately, you have a chance
to relearn it now. You should do that ... it'll be important in any math
course you ever take.

'm' is the slope of the line on the graph.

The slope is

      (the change in 'y' between any two points on the line)
divided by
   (the change in 'x' between the same two points).

You can choose any two points on the line, and the slope is always the same.

To make it easy, look at the two points on this graph where the line crosses
the x-axis and the y-axis.

Going between these two points ...
-- the line goes up, from y=0 to y=4. The change in 'y' is 4 .
-- the line goes to the right, from x=-2 to x=0. The change in 'x' is 2 .

   'm' = the slope = (4)/(2) = 2 .

The "y-intercept" is the place where the line crosses the y-axis.
On this graph, that's the point where y=4 .

The equation of EVERY straight line on ANY graph is:

   Y = (the slope) times 'x' + (the y-intercept) .

So the equation of THIS line on THIS graph is

   Y = 2x + 4 .

Vertex (0,0) focus (0,-1)A) y=1/4 x^2
B) y=-1/4x^2
C) y=1/16x^2
D) y=-1/16x^2

Answers

Answer:B

Step-by-step explanation:

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C.2,3
D. 3,4

Answers

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The point is closest to the value "2" on the x axis.
The point is closest to the value "3" on the y axis.

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Which equation is true when b = -4?A b/4 + 5.5 = 4.5
B -54 + 2b = -46
С 7b - 8 = -20
D b/8 - 6 = -8

Answers

Answer:

Step-by-step explanation:

-4/4 = -1

-1+5.5

=4.5

The answer is B. -54+2b=-46

What number is 0.4% of 20?

Answers

The solution is, 0.08 which is 0.4% of 20.

What is percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

to find the number which is 0.4% of 20.

so, we get,

let, the number be x

now, 20* 0.4% = x

or, 20/100= x/0.4

then cross multiply 20/250=x

x = 0.08

which 0.08

Hence, the answer is 0.08

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20/100= x/0.4 then cross multiply 20/250=x which 0.08 the answer is 0.08

Susu is solving the quadratic equation 4x2 – 8x – 13 = 0 by completing the square. Her first four steps are shown in the table.In which step did Susu first make an error?

Step 1
Step 2
Step 3
Step 4

Answers

In the question "Susu is solving the quadratic equation 4x2 – 8x – 13 = 0 by completing the square. Her first four steps are shown in the table. In which step did Susu first make an error?" Susu made her first error in step 2, when she factored out 4 she is supposed to divide 8x by 4. Thus the correct expression for step 2 should be 4(x^2 - 2x) = 13 To complete the solution for the equation: 4(x^2 - 2x + 1) = 13 + 4(1) 4(x - 1)^2 = 13 + 4 4(x - 1)^2 = 17 (x - 1)^2 = 17/4 x - 1 = +/- sqrt(17/4) x = 1 +/- sqrt(17) / 2

Answer:B

Step-by-step explanation:

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