Answer:
Equation of line u in slope-intercept form is: [tex]\mathbf{y=\frac{1}{2}x+9 }[/tex]
Step-by-step explanation:
Equation of line t : y = -2x + 9.
We need to find equation of line u, which is perpendicular to line t and passes through point (-10,4)
The equation must be in slope-intercept form.
The general equation of slope-intercept form is: [tex]y=mx+b[/tex] where m is slope and b is y-intercept
Finding Slope:
If two lines are perpendicular, their slopes are opposite i.e [tex]m=-\frac{1}{m}[/tex]
Slope of line t: y=-2x+9 we get m =-2 (Comparing with general form y=mx+b, we get m =-2)
Slope of line u: [tex]\frac{1}{2}[/tex]
So, we get Slope of line u: m= [tex]\frac{1}{2}[/tex]
Finding y-intercept:
Using slope m= [tex]\frac{1}{2}[/tex] and point(-10,4) we can find y-intercept
[tex]y=mx+b\\4=\frac{1}{2}(-10)+b\\4=-5+b\\b=4+5\\b=9[/tex]
Equation of line u:
So, equation of line u, having slope m= [tex]\frac{1}{2}[/tex] and y-intercept b=9, we get:
[tex]y=mx+b\\y=\frac{1}{2}x+9[/tex]
So, Equation of line u in slope-intercept form is: [tex]\mathbf{y=\frac{1}{2}x+9 }[/tex]
