Question

please help me i am confuse
write the equation of the line through (1,7) perpendicular to -5x-4y=23

Answer 1

You have a line and a point on the line. Rewrite\[-5x-4y=23\]as\[-4y=5x+23\]\[y=(-5/4)x-23/4\]giving the slope of the line as -5/4. The rule is that perpendicular lines have the product of their gradients equaling -1 ( except if one has gradient zero then the other is vertical ). So the desired gradient of that perpendicular line is 4/5. So the equation of the line has the form \[y=(4/5)x + c\]for some c that we have to find. But we know this line also goes through the point (1,7), hence \[7=(4/5)1 +c\]\[c=7-4/5=(35-4)/5)=31/5\]so the complete equation is \[y=(4/5)x +31/5\]

Answer 2

i think its not right

Answer 3

you suppose to use y-y1+m(x-x1) after you figure out the slope

Answer 4

Ha! :-)

(1,7) isn't on the line\[-5x-4y=-5-28\neq 23\]it would be if it were (1,-7) though, giving\[y=(4/5)x + c\]\[-7=(4/5)1+c\]\[c=(-35+4)/5=-31/5\]