Write the equation of a line with a slope of 1/7 and passes through the point (2,5)

Answer 1

There are two ways to write an equation with a given slope and point. One way is using point-slope form of a line:

y - y₁ = m (x - x₁)

x₁ = 2

y₁ = 5

m = 1/7

y - 5 = (1/7)(x - 2)

Distribute (1/7):

y - 5 = (1/7)x - (2/7)

Add 5 to both sides:

y = (1/7)x + (33/7)

The other way is by plugging in the m (slope), and the x and y from the point into slope-intercept form y = mx + b and solve for the y-intercept b.

x = 2

y = 5

m = 1/7

5 = (1/7)(2) + b

5 = (2/7) + b

Subtract (2/7) from both sides:

33/7 = b

Then rewrite the equation using the given slope 1/7 and the newly found y-intercept 33/7

y = (1/7)x + 33/7

Answer 2

Method 1 :

Given the slope m = 1/7

and the points (x', y') = (2, 5)

Using the formula y-y' =m(x-x')

implies y-5 = 1/7(x-2)

hence y-5 = 1/7x-2/7

Now multiply both sides by the value of 7

We have 7y-35 = x-2

7y-33 = x

7y =x +33

y = 1/7 + 33/7 which is the equation

Method 2:

Using the equation of a straight line

y = mx + c

Now plugging in the values (2, 5) into the equation for values of x and y to find the variable c; and the value of the slope 1/7

5 = 1/7(2) + c

5 = 2/7 + c

5/1 -2/7 = c

c = 33/7.

Hence the equation in the form y = mx + c can written as y = 1/7x + 33/7 which is the equation of the line with the slope of 1/7 passing through the point (2,5).

Answer 3

There are multiple ways to approach this problem. Given that you have a point and a slope, the easiest way is to use the point slope formula. Point slope formula is as follows: y-y1=m(x-x1) where m is the slope and (x1,y1) is the point on the line. Using this you would have y-5=1/7(x-2). You have now written the equation of a line with a slope of 1/7 that goes through the point (2,5). If you want to take it further, you can solve the equation for y in order to get the equation in slope-intercept form. In order to do this, you would have to distribute the 1/7 so you would get y-5=1/7x-2/7. From here you would add 5 to both sides in order to isolate the y. You would get y=1/7x+4_5/7 where 1/7 is the slope and 4 and 5/7 is the y-intercept.