Question

How do you write an equation of a line with slope = 2 and contains point (-1 , 4)?

Answer 1

`y=2x+6`

Explanation:

The general format for the point-intercept quation is `y=mx+b`

Where `m=`slope and `b=`y-intercept

Given the slope is `2`, the equation now looks like `y=2x+b`

Given `P(-1,4)` we can solve for the `b` variable by substituting the `x` and `y` cordinates.

`4=2*(-1)+b`
`4=-2+b`
`b=6`

Therefore the equation that has the slope of `2` and passes through the point `(-1,4)` is `y=2x+6`

Here's a graphical look,

graph{2x+6 [-10, 10, -5, 10]}

Answer 2

See the entire solution process below:

Explanation:

We can use the point-slope formula to write an equation for this line. The point-slope formula states: `(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))`

Where `color(blue)(m)` is the slope and `color(red)(((x_1, y_1)))` is a point the line passes through.

Substituting the slope and values from the point in the problem gives:

`(y - color(red)(4)) = color(blue)(2)(x - color(red)(-1))`

`(y - color(red)(4)) = color(blue)(2)(x + color(red)(1))`

We can solve this equation for `y` to put the equation in slope-intercept form. The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

`y - color(red)(4) = (color(blue)(2) xx x) + (color(blue)(2) xx color(red)(1))`

`y - color(red)(4) = 2x + 2`

`y - color(red)(4) + 4 = 2x + 2 + 4`

`y - 0 = 2x + 6`

`y = color(red)(2)x + color(blue)(6)`