Answer:
The equation in slope-intercept form of required line is: [tex]\mathbf{y=\frac{2}{3}(x)-6}[/tex]
Step-by-step explanation:
We need to write equation in slope-intercept form to represent the line on the graph.
The general equation in slope-intercept form is: [tex]y=mx+b[/tex]
Where m is slope and b is y-intercept
Finding slope using formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\[/tex]
Looking at he graph we have
[tex]x_1=3, y_1=-4, x_2=6, y_2=-2[/tex]
Putting values in formula and finding slope:
[tex]Slope=\frac{-2-(-4)}{6-3}\\\\Slope=\frac{-2+4}{3}\\Slope=\frac{2}{3}[/tex]
So, we get slope m = 2/3
Using slope m=2/3 and point (3,-4) we can find y-intercept
[tex]y=mx+b\\\\-4=\frac{2}{3}( 3)+b\\-4=2+b\\b=-4-2\\b=-6[/tex]
So, y-intercept b = -6
The equation of line having m=2/3 and b=-6 will be:
[tex]y=mx+b\\y=\frac{2}{3}(x)-6[/tex]
The equation in slope-intercept form of required line is: [tex]\mathbf{y=\frac{2}{3}(x)-6}[/tex]
