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The point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ is $\fbox{\begin\\\ \math 2x+5y=-15\\\end{minispace}}$ i.e., $\fbox{\begin\\\ \bf option C\\\end{minispace}}$ .

Further explanation:

It is given that line passes through the points $(-5,-1)$ and $(10,-7)$ .

The objective is to determine the point slope form of the line which passes through the points $(-5,-1)$ and $(10,-7)$ .

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 $(-5,-1)$ as $(x_{1},y_{1})$ and $(10,-7)$ as $(x_{2},y_{2})$ .

Slope of a curve is defined as the change in the value of $y$ with respect to change in value of $x$ .

The slope of the line is calculated as follows:

$\fbox{\begin\\\ \math m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\end{minispace}}$

To obtain the value of slope substitute the value of $x_{1},y_{1},x_{2},y_{2}$ in the above equation.

$\begin{aligned}m&=\dfrac{-7-(-1)}{10-(-5)}\\&=\dfrac{-6}{15}\\&=\dfrac{-2}{5}\end{aligned}$

Therefore, the slope of the line is $\fbox{\begin\\\ \math m=\dfrac{-2}{5}\\\end{minispace}}$

The general way to express the equation of a line in its point slope form is as follows:

$\fbox{\begin\\\ \math (y-y_{1})=m(x-x_{1})\\\end{minispace}}$

To obtain the point slope form of the equation of the line substitute the value of $m$ , $x_{1}$ and $y_{1}$ in the above equation.

$\begin{aligned}(y-(-1))&=\dfrac{-2}{5}(x-(-5))\\(y+1)&=\dfrac{-2}{5}(x+5)\\5y+5&=-2x-10\\5y+2x&=-15\end{aligned}$

From the above calculation it is concluded that the point slope form the equation of a line is $\fbox{\begin\\\ \math 5y+2x=-15\\\end{minispace}}$

Figure 1 (attached in the end) represents the graph of the function $5y+2x=-15$ .

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 $(-5,-1)$ and $(10,-7)$ is $2x+5y=-15$ i.e., option C.

Learn more:

1. A problem to complete the square of quadratic function brainly.com/question/12992613

2. A problem to determine the slope intercept form of a line brainly.com/question/1473992

3. Inverse function 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.

6 0

3 years ago

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Anyone know the answer?

FrozenT [24]

I legit can’t see it

8 0

3 years ago

Saige's spaceship traveled 588588588 kilometers (\text{km})(km)left parenthesis, start text, k, m, end text, right parenthesis i

lesantik [10]

Answer:

A is proportional

B and C are NOT proportional

Step-by-step explanation:

First, simplify 588 and 60:

588 divided by 6

60 divided by 6

= 98

10

Simplify them again by dividing them both by 2

= 49

5

Let's look at A:

441 and 45

Simplify by dividing by 9

= 49

5

It's pretty obvious that A is proportional because the simplified values are exactly the same.

Next, let's check B:

215 and 25

Simplify by dividing by 5

= 43

5

Now that its simplified you can compare

43 is smaller than 49

5 5

B is not proportional

Finally, let's check C:

649 and 110

Simplify by dividing by 11

= 51

10

Make 51 and 49 have the same denominator so we can compare them

10 5

51 can stay the same because 5 times 2 equals 10

10

49 times 2

5 times 2

= 98

10

Now that the denominators are the same we can compare

51 is much smaller than 98

10 10

Therefore, C is also not proportional.

Hope that helps :D

8 0

3 years ago

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