Which equation represents a line that passes through the points (4, 5) and (6, 9)?

Answer 1

You need to find a slope of a line first.

m= (y₂ - y₁) /(x₂ - x₁)

(4,5) , (6, 9) so m = (9-5)/(6-4) = 4/2 = 2

1st way: (Slope- Intercept form)

y = mx +b

Pick either (4,5) or (6,9) [It does not matter which point you select]

Let's pick (4,5), and substitute for x and y in the equation y=mx+b [we know the slope and a point, we are looking for b]

5= 2(4) + b so 5 = 8 + b, then b = - 3

Equation : y= 2x - 3

2nd way: (Point- Slope form)

y - y₁ = m (x - x₁)

Pick either (4,5) or (6,9) [It does not matter which point you select]

Let's pick (4,5) and substitute for x₁ and y₁ in the equation [we have the slope and a point]

y - 5 = 2 (x - 4) [that's the equation of the line]

If you continue, you will get the exact format of the equation given firstly.

(distribute 2 over (x-4))

y - 5 = 2x - 8 (add 5 to both sides)

then

y = 2x -3

Answer 2

(4,5) and (6,9) have a line through them

y-5 = [(9-5)/(6-4)](x-4)

y-5 = 2(x-4) in point slope form, slope =2

or

y = 2x-3 in slope intercept form

or

2x-y =3 in standard form