Respuesta :
The point slope form of the line which passes through the points [tex](-5,-1)[/tex] and [tex](10,-7)[/tex] is [tex]\fbox{\begin\\\ \math 2x+5y=-15\\\end{minispace}}[/tex] i.e., [tex]\fbox{\begin\\\ \bf option C\\\end{minispace}}[/tex].
Further explanation:
It is given that line passes through the points [tex](-5,-1)[/tex] and [tex](10,-7)[/tex].
The objective is to determine the point slope form of the line which passes through the points [tex](-5,-1)[/tex] and [tex](10,-7)[/tex].
The options given are as follows:
Option A: 2x-5y=-15
Option B: 2x-5y=-17
Option C: 2x+5y=-15
Option D: 2x+5y=-17
Consider the point [tex](-5,-1)[/tex] as [tex](x_{1},y_{1})[/tex] and [tex](10,-7)[/tex] as [tex](x_{2},y_{2})[/tex].
Slope of a curve is defined as the change in the value of [tex]y[/tex] with respect to change in value of [tex]x[/tex].
The slope of the line is calculated as follows:
[tex]\fbox{\begin\\\ \math m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\end{minispace}}[/tex]
To obtain the value of slope substitute the value of [tex]x_{1},y_{1},x_{2},y_{2}[/tex] in the above equation.
[tex]\begin{aligned}m&=\dfrac{-7-(-1)}{10-(-5)}\\&=\dfrac{-6}{15}\\&=\dfrac{-2}{5}\end{aligned}[/tex]
Therefore, the slope of the line is [tex]\fbox{\begin\\\ \math m=\dfrac{-2}{5}\\\end{minispace}}[/tex]
The general way to express the equation of a line in its point slope form is as follows:
[tex]\fbox{\begin\\\ \math (y-y_{1})=m(x-x_{1})\\\end{minispace}}[/tex]
To obtain the point slope form of the equation of the line substitute the value of [tex]m[/tex], [tex]x_{1}[/tex] and [tex]y_{1}[/tex] in the above equation.
[tex]\begin{aligned}(y-(-1))&=\dfrac{-2}{5}(x-(-5))\\(y+1)&=\dfrac{-2}{5}(x+5)\\5y+5&=-2x-10\\5y+2x&=-15\end{aligned}[/tex]
From the above calculation it is concluded that the point slope form the equation of a line is [tex]\fbox{\begin\\\ \math 5y+2x=-15\\\end{minispace}}[/tex]
Figure 1 (attached in the end) represents the graph of the function [tex]5y+2x=-15[/tex].
This implies that the correct option for the point slope form of the line is option C.
Therefore, the point slope form of the line which passes through the points [tex](-5,-1)[/tex] and [tex](10,-7)[/tex] is [tex]2x+5y=-15[/tex] i.e., option C.
Learn more:
1. A problem to complete the square of quadratic function https://brainly.com/question/12992613
2. A problem to determine the slope intercept form of a line https://brainly.com/question/1473992
3. Inverse function https://brainly.com/question/1632445.
Answer details
Grade: High school
Subject: Mathematics
Chapter: Linear equation
Keywords: Equation, linear equation, slope, intercept, x-intercept, y-intercept, intersect, graph, curve, slope intercept form, line, y=3x/2-3, standard form, point slope form.
