(1,6), y=4x-2 and (2,3),y=-7/5x-4?

Question

Write the slope-intercept form of an equation of the line that passes through the given point and is parellel to the graph of each equation.

Answer 1

(1,6), m = 4
6 = 4(1) + b
6 = 4 + b
2 = b

ANS : y = 4x + 2

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

(2,3), m = (-7/5)
3 = (-7/5)(2) + b
3 = (-14/5) + b
15 = -14 + 5b
29 = 5b
b = (29/5)

ANS : y = (-7/5)x + (29/5)

Answer 2

parallel means the slopes are the same
Your equations are in the form y = mx + b, where m is the slope.
The slope of the first equation is 4.
Use the equation
y - y1 = m(x-x1), where m is the slope and (x1,y1) is the given point.
y - 6 = 4(x-1)
Distribute the 4 on the right side
y - 6 = 4x - 4
Add 6 to each side
y = 4x + 2

The slope of the second equation is -7/5
y - 3 = (-7/5)(x-2)
Distribute the -7/5 on the right side
y - 3 = (-7/5)x + 14/5
Add 3 to each side and get a common denominator.
y = (-7/5)x + 14/5 + 15/5
y = (-7/5)x + 29/5

Answer 3

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

when two lines are parallel, the slopes are equal

line parallel to y = 4x-2 is of the form y=4x+b since this passes through (1,6) we get 6 = (4*1) + b

therefore b =2

required line is y = 4x +2
-------------------------------------------------

similarly
line parallel to y= -7/5x-4 is of the form y= -7/5x +c, since this passes through (2,3) we get 3 = (-7/5)*2 +c and this gives c = 29/5

so that the required equation is y = (-7/5)x +29/5

Answer 4

y=4x+b, substitute 1 for x and 6 for y

6 = 4 + b, so b = 2 and the equation is y = 4x + 2


y = -7/5 x -4 substitute 2 for x and 3 for y

3 = -7/5 (2) + b, so b = 5 4/5 and the equation is y = -7/5 x + 29/5