x=4, y=9 (4,9)
If 8x + 4y = 16, then y = - 2x + 4 Thus the slope is -2 and the intercept is 4.
-8x + 4y = 28 Add 8x to each side: 4y = 8x + 28 Divide both sides by 4: y = 2x + 7
Equations: y = x+4 and x^2 +y^2 -8x +4y = 30 It appears that the given line is a tangent line to the given circle and the point of contact works out as (-1, 3)
They are perpendicular lines because the slopes are 3/4 and -4/3 respectively.
x=4, y=9 (4,9)
If 8x + 4y = 16, then y = - 2x + 4 Thus the slope is -2 and the intercept is 4.
-8x + 4y = 28 Add 8x to each side: 4y = 8x + 28 Divide both sides by 4: y = 2x + 7
(8 + 4) x 5...
(0,-4)
Equations: y = x+4 and x^2 +y^2 -8x +4y = 30 It appears that the given line is a tangent line to the given circle and the point of contact works out as (-1, 3)
They are perpendicular lines because the slopes are 3/4 and -4/3 respectively.
Put in this form to see. Y = mX + c 3X - 4Y = - 3 - 4Y = - 3X - 3 Y = (3/4)X + 3/4 --------------------- 8X + 6Y = 14 6Y = - 8X + 14 Y = (- 4/3)X + 7/3 ----------------------- Closer to perpendicular than anywhere near parallel!
4y = 8x Divide each side by 4: y = 2x Draw a straight line, through the origin, with a slope of +2 .
(4x + 12)/(8x - 4y) = [4(x) + 4(3)]/(4(2)(x) - 4y] = 4(x + 3)/4(2x - y) = (x+ 3)/(2x - y)
(4, 8)
y=4x=1Because:8x - y = 45x + 3y = 17You can rearrange the first equation to give:y = 8x - 4And substitute this into the second equation:5x + 3(8x - 4) = 17Expanded out:5x + 24x - 12 = 1729x - 12= 1729x = 29So x=1And because you know know x you can put that into an equation to find y:y = 8x - 4y= 8 - 4y= 4