Question

Slope intercept of (2,-12) and (5,6)

Answer 1

y = 6x - 24

Explanation:

the equation of a line in slope-intercept form is

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (2, - 12 ) and (x₂, y₂ ) = (5, 6 )

m =
`(6+12)/(5-2)` =
`(18)/(3)` = 6

y = 6x + c ← is the partial equation

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

using (5, 6 ), then

6 = 30 + c ⇒ c = 6 - 30 = - 24

y = 6x - 24 ← equation in slope-intercept form

Answer 2

The slope of the line is m=6.

The y-intercept is (0,−24).

The equation of the line in the slope-intercept form is y=6x−24.

Explanation:

The slope of the line passing through the two points P=(x1,y1) and Q=(x2,y2) is given by m=y2−y1x2−x1.

We have that x1=2, y1=−12, x2=5, y2=6.

Plug the given values into the formula for the slope: m=(6)−(−12)(5)−(2)=183=6.

Now, the y-intercept is b=y1−m⋅x1 (or b=y2−m⋅x2, the result is the same).

b=−12−(6)⋅(2)=−24.

Finally, the equation of the line can be written in the form y=mx+b.

y=6x−24.

Answer:

The slope of the line is m=6.

The y-intercept is (0,−24).

The equation of the line in the slope-intercept form is y=6x−24.