Question

How would you graph this y-3=4/3(x+2)

Answer 1

The line passes through
`(-(17)/(4),0)\ and\ (0,(17)/(3))`.

Graph is attached.

Explanation:

Line passing through the point
`(x_1,y_1)` and slope
`m`:

`y-y_1=m(x-x_1)`

`Compare\ y-3=(4)/(3)(x+2)\ with\ the\ standard\ form\\\\x_1=-2,\ y_1=3\ and\ m=(4)/(3)\\\\This\ is\ equation\ of\ line\ passing\ through\ (-2,3)\ and\ having\ slope(m)=(4)/(3)\\\\Slope=\tan \theta\\\\\tan\theta=(4)/(3)\\\\\theta=\tan^(-1) (4)/(3)\\\\\theta=53.13\textdegree\\\\Hence\ line\ passes\ through\ (-2,3)\ and\ makes\ an\ angle\ 53.13\textdegree\ with\ the\ x-axis`

Sketch:

Y-intercept:

`substitute\ x=0\\\\y-3=(4)/(3)* 2\\\\y=(8)/(3)+3\\\\y=(17)/(3)\\\\line\ passes\ through\ (0,(17)/(3)).`

x-intercept:

`substitute\ y=0\\\\-3=(4)/(3)(x+2)\\\\x+2=-(3)/(4)* 3\\\\x=-(9)/(4)-2\\\\x=-(17)/(4)\\\\Line\ passes\ through\ (-(17)/(4),0).`

Sketch the line passes through
`(-(17)/(4),0)\ and\ (0,(17)/(3))`.