Question

the point slope form of the equation of the line that passes through (-5,-1) and (10,-7) is y+7=-2/5(x-10) what is the standard from of the equation

Answer 1

Answer:

the standard form of the equation is: $2x+5y=-15$

Step-by-step explanation:

we know that the standard equation of a line is given by $ax+by=c$

so, on converting the above point slope form of the equation of the line that passes through (-5,-1) and (10,-7) i.e. $y+7=\frac{-2}{5} (x-10)$ into the standard form of the equation.

firstly we'll multiply both side of the equation by 5 to have

$5(y+7)=-2(x-10)$

$5y+35=-2x+20\\2x+5y=20-35\\2x+5y=-15$

Hence, the standard form of the given equation of line is:  $2x+5y=-15$.

Answer 2

The standard form of the equation is $\boxed{2x + 5y = - 15}.$ Option (c) is correct.

Further explanation:

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

$\boxed{y = mx + c}$

The standard form of the linear equation can be expressed as follows,

$\boxed{ax + by = c}$

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,

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

Given:

The passes through the points are $\left( { - 5, - 1} \right)$ and $\left( {10, - 7} \right).$

The point slope form of the equation is $y + 7 = - \dfrac{2}{5}\left( {x - 10} \right).$

Explanation:

Solve the point slope form$y + 7 =  - \dfrac{2}{5}\left( {x - 10} \right)$.

$\begin{aligned}y + 7&=- \frac{2}{5}\left( {x - 10} \right)\\5\left( {y + 7} \right) &=  - 2x + 20\\5y + 35 &= - 2x + 20 \\5y + 2x &= 20 - 35 \\ 2x + 5y &=- \15\\\end{aligned}$

The standard form of the equation is $\boxed{2x + 5y =  - 15}$. Option (c) is correct.

Learn more:

1. Learn more about inverse of the function https://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

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