Question

How do you write a equation in slope intercept form of the line passing through the given points (0,7) , (1,9)?

Answer 1

`y =2x+7`

Explanation:

Given
`color(white)("XXX")(x_1,y_1)=(0,7)` and
`color(white)("XXX")(x_2,y_2)=(1,9)`

The (y) intercept is the value of `y` when `x=0`
`color(white)("XXX")`given the point `(x_1.,y_1)=(0,7)`
`color(white)("XXX")`the (y)intercept is `b=7`

The slope of a line between two points is
`color(white)("XXX")m=(y_2-y_1)/(x_2-x_1)`
`color(white)("XXX")`for the given points (above), the slope is
`color(white)("XXX")m=(9-7)/(1-0)=2`

The slope-intercept form for a line with slope `m` and (y) intercept `b` is
`color(white)("XXX")y=mx+b`
`color(white)("XXX")`using the values we have just determined for `m` and `b`
`color(white)("XXX")y=2x+7`