Question

How do you find the slope and y intercept for `y = -2x + 7`?

Answer 1

`color(purple)("Look at the very detailed method used/explained in my solution.")`

Explanation:

`color(blue)("Slope or gradient")`
The slope is the amount of up or down for the amount of along and is directly related to the change in `x` and the change in `y`.
So if you had say, 6 down (change in y value) for 3 along (change in x value) the slope is `color(white)(..)(6 " up or down")/(3 " along")`
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But if we treat this as a ratio and divide both numerator and denominator by 3 we have:

`( 6 -: 3)/(3 -: 3) = 2/1 = 2`

So for every 1 along we have 2 up or down.
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We need to have a way of showing if the slop is upwards or downwards. The convention for this is that if we have -2 then the slope is downwards if we move from left to right. In which case +2 means upwards.
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`color(brown)("So your question has a downward slop of " -2)`
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`color(blue)("x intercept")`
This is when the line crosses the x-axis. The x-axis it at `y=0`
So to find this we substitute `y=0 " into " y=-2x+7` giving:

`0=-2x+7`
Add `2x` to both sides giving:
`0+2x=2x-2x+7`
`2x=0+7`
Divide both sides by 2 giving:
`2/2 x=7/2`
`1 xx x =7/2 = 3 1/2`
`color(brown)(x_("intercept")= 3 1/2`
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`color(blue)("y intercept")`

This when the line crosses the y-axis. The y-axis is at `x=0`. So we substitute `x=0` into `y=-2x+7` giving

`y = (2 xx 0) + 7`

`color(brown)(y_("intercept")= 7`
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