Question

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

Answer 1

Answer:

The line passes through $(-\frac{17}{4},0)\ and\ (0,\frac{17}{3})$.

Graph is attached.

Step-by-step explanation:

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

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

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

Sketch:

Y-intercept:

$substitute\ x=0\\\\y-3=\frac{4}{3}\times 2\\\\y=\frac{8}{3}+3\\\\y=\frac{17}{3}\\\\line\ passes\ through\ (0,\frac{17}{3}).$

x-intercept:

$substitute\ y=0\\\\-3=\frac{4}{3}(x+2)\\\\x+2=-\frac{3}{4}\times 3\\\\x=-\frac{9}{4}-2\\\\x=-\frac{17}{4}\\\\Line\ passes\ through\ (-\frac{17}{4},0).$

Sketch the line passes through $(-\frac{17}{4},0)\ and\ (0,\frac{17}{3})$.