Finding a slope?

Question

Find the equation for the line passing through (2,1) with slope 5/2

Answer 1

Slope Intercept formula

y= mx + b

1 =5/2(2) + b

1 = 10/2 + b

1 = 5 + b

1 - 5 = 5 + b - 5

-4 = b

The answer is b = - 4

- - - - - - - - - - - - - - - - -

The equation becomes

1 = 5/2(2) - 4

Answer 2

(y-1) = (5/2)*(x-2)
2y-2 =5x-10
2y = 5x-8
check
if 2y= 5x-8
y = (5/2)x-4
when y=mx+c... m is the slope
so in our case slope = 5/2
when the line passes through a point , if you substitute the values in the equation and simplify it should become equal to zero
or left hand side(LHS) value should equal the right hand side(RHS) value
in our case the point is (2,1) means x=2, y=1
substituting these values in the equation
LHS = y = 1
RHS = (5/2)*2 - 4 = 5-4 = 1
LHS = RHS .....so the answer is correct i.e
the equation of the line passing through (2,1) and with slope 5/2 is 2y = 5x -8 or y = (5/2) x- 4

Answer 3

Equation of slope:

Y = mX + b

slope = m = 5/2
Y = 1
X = 2

substitute

1 = 5/2 * 2 + b

therefore b (y-intercept) is = -4


the equation of the line therefore is :

Y = 5/2X - 4

Answer 4

The slope-intercept form:
y=mx+b

The formula to finding the equation:
(y-y1)=m(x-x1)

Since x1=2, y1=1, and m=5/2 you do this:

y-1=(5/2)(x-2)
y-1=5/2x-5
y=5/2x-4

Check:
1=5/2(2)-4
1=5-4
1=1

I hope this helps!

Answer 5

y = mx + c (where m = slope and c = y intercerpt when x = 0)

putting values

1 = (5/2)*2 + C
1 = 5 + C
1-5 = 5 + C - 5
C = -4

Final equation:

y = (5/2)x - 4

Answer 6

y = mx + c
Thus, 1 = (5/2) * 2 + c
so, c = -4.
The equation is therefore: y = (5/2)x - 4
or, 2y - 5x + 8 = 0