Question

Write the slope intercept form of the equation of the line through (2,1) and (4,5)
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Answer 1

y=2x-3

Explanation:

Slope formula:

`\sf{(Y_2-Y_1)/(X_2-X_1)`

y2=5

y1=1

x2=4

x1=2

Solve.

5-1/4-2

Subtract.

5-1=4

4-2=2

Divide.

4/2=2

The slope is 2.

You have to solve with slope-intercept form.

`\sf{y=mx+b}`

m represents the slope.

b represents the y-intercept.

y-intercept is -3.

`\sf{\boxed{y=2x-3}`

So, the correct answer is y=2x-3.

Answer 2

`y=2x-3`

Explanation:

Hi there!

Slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Determine the slope (m)

`m=(y_2-y_1)/(x_2-x_1)` where the two given points are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the given points (2,1) and (4,5)

`m=(5-1)/(4-2)\\m=(4)/(2)\\m=2`

Therefore, the slope of the line is 2. Plug this into
`y=mx+b` :

`y=2x+b`

2) Determine the y-intercept (b)

`y=2x+b`

Plug in one of the given points and isolate b

`1=2(2)+b\\1=4+b`

Subtract both sides by 4

`1-4=4+b-4\\-3=b`

Therefore, the y-intercept of the line is -3. Plug this into
`y=2x+b`:

`y=2x-3`

I hope this helps!