Question

The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y plus 7 equals negative StartFraction 2 over 5 EndFraction left-parenthesis x minus 10 right-parenthesis.. What is the standard form of the equation for this line?

2x – 5y = –15
2x – 5y = –17
2x + 5y = –15
2x + 5y = –17

Answer 1

An equation in standard form that passes through (-5,-1) and (10,-7) is:

2x + 5y = -15

Further explanation

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

m → gradient of the line

( 0 , c ) → y - intercept

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

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

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

$\large {\boxed{y - y_1 = m ( x - x_1 )}}$

Let us tackle the problem.

This probem is about Linear Equation.

Let:

( -5 , -1 ) → ( x₁ , y₁ )

( 10, -7 ) → ( x₂ , y₂ )

We will use the formula as follows:

$y - y_1 = \frac{y_2 - y_1}{x_2 - x _1} \times ( x - x_1 )$

$y - (-1) = \frac{-7 - (-1)}{10 - (-5)} \times ( x - (-5) )$

$y + 1 = \frac{-6}{15} \times ( x + 5 )$

$y + 1 = \frac{-2}{5} \times ( x + 5 )$

$5( y + 1 ) = -2 ( x + 5 )$

$5y + 5 = -2x - 10$

$2x + 5y = - 10 - 5$

$2x + 5y = - 15$

$\texttt{ }$

Learn more

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point

Answer 2

Answer:

C

Step-by-step explanation:

2x + 5y = –15