Write the equation of a line in slope-intercept form passing through (4, 5) and (6, 8)

y = 3/2 x-1 ..

Step-by-step explanation:

First find the slope.

m = y2-y1/x2-x1

x1 = 4 , x2 = 6

y1 = 5, y2 = 8

m = 8-5/ 6-4

m = 3/2

Slope intercept form of linear equation:

y = mx+b

5 = 3/2 * 4 +b

5 = 12/2 +b

5 = 12+2b/2

10 =  12+2b

10-12 = 2b

-2 = 2b

Divide both sides by 2.

-2/2 = 2b/2

-1 = b

Thus slope intercept form of equation is:

y = 3/2 x-1

Step-by-step explanation:

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

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

Knowing that this line passes through the points (4, 5) and (6, 8), we can find the slope with the formula . Then:

Substitute one point and the slope into   and solve for "b":

Then, the equation of this line in Slope-Intercept form is:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4