Answer:
An equation of a line with slope -3/2 and x-intercept (4,0) will be:
[tex]y\:=\:-\frac{3}{2}x\:+\:6[/tex]
Step-by-step explanation:
The slope-intercept form of the line equation
y = mx+b
where
Given
now substitute m = -3/2 and the point (4, 0) in the slope-intercept form of line equation
[tex]y = mx+b[/tex]
[tex]0\:=\:-\frac{3}{2}\left(4\right)\:+\:b\:\:\:\:\:[/tex]
[tex]-6+b=0[/tex]
Add 6 to both sides
[tex]-6+b+6=0+6[/tex]
Simplify
[tex]b=6[/tex]
Thus, the y-intercept b = 6
now substitute m = -3/2 and b = 6 in the slope-intercept form of line equation
[tex]y = mx+b[/tex]
[tex]y\:=\:-\frac{3}{2}x\:+\:6[/tex]
Therefore, an equation of a line with slope -3/2 and x-intercept (4,0) will be:
[tex]y\:=\:-\frac{3}{2}x\:+\:6[/tex]
