Line gh passes through points (2,5) and (6,9). which equation represents line gh?

Equation of line GH is y=x+3.

Step-by-step explanation:

Equation of any line can be represented in the form y=mx+b where m is the slope and b is the y intercept.

The given line is passing through the points ( 2,5) and (6,9).

Slope =m = (9-5)÷(6-2) =1.

The given line passes through the point (2,5) and m=1.

Substituting the values of m,x,y in y=mx+b we have:

5=1(2)+b

Or, 5=2+b ,

Or b=3 .

Line GH has slope m=1 and y intercept b=3 .

Hence equation of line GH is y=x+3.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: