Question

What is the equation of the line that passes through the point (−3,4) and has a slope of 1 ?

Answer 1

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We have following equation to find the point-slope form of the linear functions.

`y - y(0) = m * ( \: x - x(0) \:)`

In which :

`y(0) = y \: \: given \: \: point = 4`

`x(0) = x \: \: given \: \: point = - 3`

`m = slope = 1`

Now just need to put the coordinates and the slope in the above equation.

`y - 4 = 1 * ( \: x - ( - 3) \: )`

`y - 4 = x + 3`

Add sides 4

`y - 4 + 4 = x + 3 + 4`

`y = x + 7`

Done...

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Answer 2

y = x + 7

Explanation:

The equation of a line in slope- intercept form is

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

Here m = 1, thus

y = x + c ← is the partial equation

To find c substitute (- 3, 4) into the partial equation

4 = - 3 + c ⇒ c = 4 + 3 = 7

y = x + 7 ← equation of line