Mathematics: 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?

The point-slope form of the equation of the line

Ответ:

vso227

03.01.2022

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:

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

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

Therefore, the slope is $\dfrac{1}{4}$ .

The point-slope form of the equation of a line with slope 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 ${x_1}$ , for ${y_1}$ and $\frac{1}{4}$ for in equation (2) to obtain the equation of line.

$\begin{aligned}y - 1&=\frac{1}{4}\left({x - 12}\right)\\4\left({y - 1}\right)&=x - 12\\4y - 4&=x - 12\\x - 4y&=8\\\end{aligned}$

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 $\boxed{{\mathbf{x - 4y = 8 }}}$

Learn more:

1. Which classification best describes the following system of equations?

2. What is the value of in the equation when ?

3. What are the values of x?

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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Ответ:

Serenitybella

03.01.2022

Mathematics

I think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). Because if you replace x by -4 your are supposed to find y=-3 which is not the case her. If you replace x by -4 you find =-15.
I assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how I found that out I can tell you).
In this equation if I replace x by -4 I find y=-3 and if I replace x by 12, I find y=1 so the line representing this equation is passing through those 2 points.
Then the standard form of the equation is finding an expression of y in function of x
y-1=1/4*(x-12)
y=x/4-3+1
y=x/4-2

Hope that helps.
Do you confirm there was a mistake in the question?

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Ответ:

lesleyy7278

28.08.2020

Mathematics

Kentucky Avenue is 575 ft between C street and D street

Step-by-step explanation:

x / (460 ft) = (1000 ft) / (800 ft)

Divide the right side:

x / (460 ft) = 1.25

To solve for "x", multiply both sides by 460 ft:

(460 ft) [x/(460)] = (460) (1.25)

x = 575 ft

Hope this helped :)

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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?

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