Question

Which equation represents the line passes through points (1,-5 and (3,-17

Answer 1

(1,-5)(3,-17)
slope = (-17 - (-5) / (3 - 1) = - 12/2 = - 6

y = mx + b
slope(m) = -6
use either of ur points...(1,-5)...x = 1 and y = -5
now we sub and find b, the y int
-5 = -6(1) + b
-5 = -6 + b
-5 + 6 = b
1 = b

so ur equation is : y = -6x + 1....or 6x + y = 1

Answer 2

The equation of the line that passes through the points $\left( {1, - 5} \right)$ and $\left( {3, - 17} \right)$ is $\boxed{y= -6x + 1}.$

Further  explanation:

The linear equation with slope m and intercept c is given as follows.

$\boxed{y = mx + c}$

The formula for slope of line with points $\left( {{x_1},{y_1}} \right)$ and $\left({{x_2},{y_2}}\right)$ can be expressed as,

$\boxed{m=\dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}$

Given:

The passes through the points are  $\left({1, - 5}\right)$ and $\left({3, - 17}\right).$

Explanation:

The line passes the points that are  $\left({1, - 5}\right)$ and $\left( {3, - 17}\right).$

The slope of the line can be obtained as follows.

$\begin{aligned}m&=\frac{{-17-\left( { - 5}\right)}}{{\left( 3 \right) - 1}}\\&=\frac{{ - 12}}{2}\\&=- 6\\\end{aligned}$

The slope of the line ism =  - 6.

The line passes through the point $\left({3, - 17}\right).$

Substitute 3 for x, - 6 for m and -17 for y in equation y = mx + c to obtain the value of c.

$\begin{aligned}-17&= - 6\left(3\right)+c\\- 17&=- 18+ c\\- 17 + 18 &= c\\1 &=c\\\end{aligned}$

The equation is y =  - 6x + 1.

Hence, the equation of the line that passes through the points $\left( {1, - 5}\right)$ and $\left( {3, - 17}\right)$ is $\boxed{y= -6x + 1}.$

Learn more:

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2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: numbers, slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.