Answer:
The standard form of equation of the line through the given points. through (0.-4) and (-3,-2) is [tex]\frac{2}{3}x+y=-4[/tex]
Step-by-step explanation:
The standard form of equation is [tex]Ax+By=C[/tex]
Finding slope
Using the given points (0,-4) and (-3,-2) we can find slope using formula:[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]Slope=\frac{-2-(-4)}{-3-(0)}\\Slope=\frac{-2+4}{-3} \\Slope=-\frac{2}{3}[/tex]
Finding y-intercept
Using point (0,4) and Slope=-2/3 we can find y-intercept
[tex]y=mx+b\\-4=-\frac{2}{3}(0)+b\\-4=0+b\\b=-4[/tex]
The slope intercept form of the line through the given points. through (0.-4) and (-3,-2) having slope =-2/3 and b=-4 will be:
[tex]y=mx+b\\y=-\frac{2}{3}x-4[/tex]
Now, standard form of equation will be: [tex]\frac{2}{3}x+y=-4[/tex]
So, The standard form of equation of the line through the given points. through (0.-4) and (-3,-2) is [tex]\frac{2}{3}x+y=-4[/tex]
