Part a
we have the equation
[tex]y=3x-4[/tex]so
The slope is m=3
The y-intercept is the point (0,-4)------> the value of b=-4
To graph the line, we need two points
we have one point (0,-4) y-intercept
Find out another point
For x=1
[tex]\begin{gathered} y=3(1)-4 \\ y=-1 \end{gathered}[/tex]The other point is (1,-1)
so
Plot the points (0,-4) and (1,-10
join them to graph the line
using a graphing tool
see the figure below
Part B
The equation of the line in slope-intercept form is given by
[tex]y=mx+b[/tex]we have (8, 7) and (6, -1)
step 1
Find out the slope
[tex]\begin{gathered} m=\frac{-1-7}{6-8} \\ \\ m=\frac{-8}{-2} \\ \\ m=4 \end{gathered}[/tex]step 2
Substitute given values
we have
m=2
point (8,7)
[tex]\begin{gathered} 7=8(2)+b \\ solve\text{ for b} \\ 7=16+b \\ b=-9 \end{gathered}[/tex]therefore
The equation of the line is
[tex]y=2x-9[/tex]