Question

find an equation for the line that passes through (-4, 8) and (3, -7). what is the slope? where does the line intersect the x-axis and the y-axis?

Answer 1

`(x_1;\ y_1);\ (x_2;\ y_2)\\\\the\ slope:m=(y_2-y_1)/(x_2-x_1)\\\\the\ slope\ form\ of\ the\ line:y=mx+b\\the\ point-slope\ form:y-y_1=m(x-x_1)\\-------------------\\\\(-4;\ 8)\to x_1=-4;\ y_1=8\\(3;-7)\to x_2=3;\ y_2=-7\\\\m=(-7-8)/(3-(-4))=(-15)/(3+4)=-(15)/(7)\\\\\\y-8=-(15)/(7)(x-(-4))\\\\y-8=-(15)/(7)x-(60)/(7)\\\\y=-(15)/(7)x-(4)/(7)\\\\x-intercept\ when\ y=0\\-(15)/(7)x-(4)/(7)=0\ \ \ |\cdot7\\\\-15x-4=0\ \ \ |+4\\\\-15x=4\ \ \ |:(-15)`


`x=-(4)/(15)\to\left(-(4)/(15);\ 0\right)\\\\y-intrcept\ when\ x=0\\\\y=-(15)/(7)\cdot0-(4)/(7)\\\\y=-(4)/(7)\to\left(0;-(4)/(7)\right)`