Answer:
The equation of the line is equal to
[tex]y=\frac{3}{2}x-2[/tex]
Step-by-step explanation:
we know that
The equation of the line in slope-intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope of the line
b is the y-intercept of the line ( value of y when the value of x is equal to zero)
In this problem we have
[tex]m=\frac{3}{2}[/tex]
[tex]b=-2[/tex]
so
the equation of the line is equal to
[tex]y=\frac{3}{2}x-2[/tex]
To plot the graph find the intercepts of the line
The y-intercept is the point [tex](0,-2)[/tex]
Find the x-intercept
The x-intercept is the value of x when the value of y is equal to zero
For [tex]y=0[/tex]
[tex]0=\frac{3}{2}x-2[/tex]
[tex]\frac{3}{2}x=2[/tex]
[tex]x=\frac{4}{3}[/tex]
the x-intercept is the point [tex](4/3,0)[/tex]
plot the two points and draw the line through the two points
using a graphing tool
see the attached figure
