What is the slope intercept form of an equation that passes through the point (2,6) and has a y intercept of 5?

Answer 1

Hi Jordan M.

What is the slope intercept form of an equation that passes through the point (2,6) and has a y intercept of 5?

We need Slope Intercept Form

y = mx + b

We are given the following: coordinates (2,6) and (0, 5)

That is two points and we can calculate the m as follows

Let (2, 6) be the coordinates of the first point

Let (0, 5) be the coordinates of the second point

m = (y₂ - y₁)/(x₂ - x₁)

m = (5 - 6)/(0 - 2) = -1/-2

m = 1/2

In Slope Intercept Form the y intercept is (0, b) because when set x equal to zero in

y = mx + b you get

y = b when x = 0

So for our equation when know b in y = mx + b is 5

Since we calculated the slope above as 1/2

We can plug in the values

y = mx + b

y = (1/2)x + 5

We can check by plugging in the x value for the coordinates (2, 6), to see if we obtain the given y value

So in

y = (1/2)x + 5

y = (1/2)2 + 5

y = 1 + 5

y = 6

You can graph this at Desmos.com to confirm that the equation passes through (2,6) and (0,5)

Answer 2

Hi Jordan.

The slope-intercept form is an equation of a line in the form of:

y = mx+b

Where m is the slope, and b is the y-intercept.

In the problem, it is given that b = 5. Now, we just need the slope (m).

To find the slope, we use rise/run, where you use two points on the line to find the slope.

We use two points and subtract them from each other to find the slope.

We are given 1 point: (2,6).

We are also given the other point, which is the y-intercept: (0,5).

Now, we subtract the points to find the slope:

(6 - 5)/(2-0) = 1/2

Now we have the slope, m, which is 1/2.

Your final answer is y = 1/2x + 5.

Answer 3

y= mx + b where m= slope and b = y intercept.

y=mx + 5. plug in the point to calculate m

6=m(2) +5

1=2m

m= 1/2

y=(1/2)x + 5 is the equation in slope intercept form

Answer 4

The slope intercept form is:

y = ax+b

b is already given as 5. Use (2,6) to solve for a:

6 = a(2)+5

2a = 1

a= 1/22

y = x/2 + 5