Question

What is the equation that passes through (4, 3) and (2, -1)?

Answer 1

Answer:

y = 2x - 5

Step-by-step explanation:

We are to find the equation of line the line which passes through the points (4, 3) and (2, -1).

Finding the slope:

Slope = $\frac{3-(-1)}{4-2} =2$

Substituting the coordinates of one of the given points and slope in the standard form of an equation to find the y intercept.

$y=mx+c$

$-1 = 2 (2) + c \\\\ c = - 5$

So the equation of the line would be $y=2x-5$

Answer 2

Answer: first option.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope of the line and "b" is the y-intercept.

To find "m", we need to substitute the coordinates of the points  (4, 3) and (2, -1) into this formula:

 $m=\frac{y_2-y_1}{x_2-x_1}$

We can identify that:

$y_2=-1\\y_1=3\\x_2=2\\x_1=4$

Then:

$m=\frac{-1-3}{2-4}\\\\m=2$

To find "b" we must substitute the slope and one of the given points into $y=mx+b$ and solve for "b". Then, this is:

$3=2(4)+b\\\\3-8=b\\\\b=-5$

Therefore, the equation of this line is:

$y=2x-5$