Question

Find the equation of the line that passes through points A and B​

Answer 1

Answer:

y= 2x-1

Step-by-step explanation:

We know two points on the line, so we can find the slope

(2,3) and (4,7)

The slope is found by using the slope formula

m = ( y2-y1)/(x2-x1)

m = ( 7-3)/(4-2) = 4/2 = 2

We can use the slope intercept form of the equation

y = mx+b where m is the slope and b is the y intercept

y = 2x+b

Using one of the points to substitute into the equation we can find b

3 = 2(2)+b

3 = 4+b

-1 =b

y= 2x-1

Answer 2

Answer:

y = 2x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = A (4, 7 ) and (x₂, y₂  ) = B (2, 3 )

m = $\frac{3-7}{2-4}$ = $\frac{-4}{-2}$ = 2 , then

y = 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 3 )

3 = 4 + c ⇒ c = 3 - 4 = - 1

y = 2x - 1 ← equation of line