Question

Complete the equation of the line through ( 3 , − 1 ) (3,−1)left parenthesis, 3, comma, minus, 1, right parenthesis and ( 4 , 7 ) (4,7)left parenthesis, 4, comma, 7, right parenthesis.

Answer 1

Answer:

$y=8x-25$

Step-by-step explanation:

Given the coordinates:

(3,−1) and (4,7)

To find:

The equation of line passing through the given points.

Solution:

Let us have a look at the slope intercept form of a line:

$y=mx+c$

c is the y intercept.

Where $m$ is the slope of the line passing through the points $(x_1,y_1),(x_2,y_2)$

Formula for slope is:

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

$x_1 = 3\\y_1 = -1\\x_2 = 4\\y_2 = 7$

$m=\dfrac{7-(-1)}{4-3}\\\Rightarrow m = 8$

So, equation of line becomes:

$y=8x+c$

Let us put (4, 7) to find the value of c:

$7=8\times 4 +c\\\Rightarrow c = -25$

So, the equation is:

$y=8x-25$

Answer 2

The equation of the line passing through the points (3.-1), and (4,7) is $y=8x-25$.

Given information:

The given line passes through the points (3.-1), and (4,7).

It is required to write the equation of the line.

Use the two-point form of a line to write the equation of the line:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\\y-(-1)=\dfrac{7-(-1)}{4-3}(x-3)\\y+1=8(x-3)\\y+1=8x-24\\y=8x-25$

From the above equation of the line, the slope is equal to 8.

Therefore, the equation of the line passing through the points (3.-1), and (4,7) is $y=8x-25$.

For more details, refer to the link:

https://brainly.com/question/19082942