Question

You Write the equation of a line in slope intercept form that has a slope of 3/4 and passes through -6,8

Answer 1

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

given that the slope is 3/4, m=3/4, so we know y=(3/4)x+b

given that a point it passes through is (-6,8), find the value of b that makes the equation true when x=-6 and y=8

y=(3/4)x+b

8=(3/4)(-6)+b

8=(-18/4)+b

8=(-9/2)+b

8+(9/2)=b

(16/2)+(9/2)=b

(25/2)=b

the equation is
`y=(3)/(4)x+(25)/(2)`

Answer 2

point slope form

y-y1 = m(x-x1)

y-8 = 3/4 (x--6)

y-8 = 3/4 (x+6)

distribute

y-8 = 3/4x +9/2

add 8 to each side

y = 3/4x + 9/2 + 8

y = 3/4x +9/2 + 8 *2/2

y = 3/4x + 9/2 + 16/2

y = 3/4x +25/2

this is in slope intercept form