6x+3y = -9 3y = -6x-9 y = -2x-3 Therefore the perpendicular slope is 1/2
Put in function, Y = mX + C, form. 6X + 3Y = - 9 3Y = - 6X - 9 Y = - 2X - 3 -------------------- m(slope) = - 2 ----------------------
5
With a line in the form y = mx + c, it has gradient m and the line perpendicular to it has gradient m' such that mm' = -1, ie m' = -1/m. A line through a point (x0, y0) with gradient m' has an equation of: y - y0 = m' (x - x0) which can be rearranged to a form for y = mx + c. Thus for the line 2x - 3y = 7: 2x - 3y = 7 → 3y = 2x + 7 → y = 2/3 x + 7/3 → it has gradient 2/3 → perpendicular line has gradient -3/2 → perpendicular line through (4, 9) perpendicular to 2x - 3y = 7 has equation: y - 9 = (-3/2)(x - 4) → 2y - 18 = -3(x - 4) → 2y - 18 = -3x + 12 → 2y = 30 - 3x → 3x + 2y = 30
The "point slope" formula would be used. This is Y-Y1=m(X-X1) where Y1 and X1 are points the line passes through. M is the slope, so to find the slope of a line perpendicular, take it's opposite reciprocal which would be -8x/9. So Y-(-8)=-8/9(X-18) distribute -8/9 into X-18 and add the 8 on the left side of the = to get the slope intercept form.
If you mean: 6x+3y = -9 then the perpendicular slope works out as 1/2 or 0.5
x-3y = 9 -3y = -x+9 y = 1/3x -3 Perpendicular slope = -3
6x+3y = -9 3y = -6x-9 y = -2x-3 Therefore the perpendicular slope is 1/2
If you mean point (-1, 4) and equation of 4x-3y = -9 then y = 4/3x+3 Slope of equation: 4/3 Perpendicular slope: -3/4 Perpendicular equation: y-4 = -3/4(x--1) => 4y = -3x+13
6x + 3y = -9 So 3y = -6x - 9 or y = -2x - 3 So the slope of the given line is -2 Therefore, the slope a any parallel line is also -2.
It is 3x + 5y = 155 The slope of the line 5x -3y = 9: 5x - 3y = 9 → 3y = 5x - 9 → y = 5/3 x - 3 → slope is 5/3 → slope of perpendicular line is -3/5 Intercept at x = 15 → y = 5/3 x 15 - 3 = 22 → equation of perpendicular line is: y - 22 = -3/5 (x - 15) → 5y - 110 = -3x + 45 → 3x + 5y = 155
9 (APEX)
If you mean: 3y=-x+9 then y=-1/3x+3 and the perpendicular equation is y=3x+6
The equation of a line that is perpendicular to 3y = -x + 9 and that has a y intercept of 6 is y = 3x + 6. The slope of the first line is -1/3, from the slope-intercept form y = mx + b, or y = -x/3 + 3. The perpendicular slope is 3, by negating and inverting -1/3. Add the intercept to the slope-intercept form and you get y = 3x + 6.
If you mean y = 3x+8 then the perpendicular slope will be -1/3 and the equation works out as 3y = -x+9
A linear equation in the form y = mx + c has slope m The slope m' of a line perpendicular to a line with slope m is such that m'm = -1 → m' = -1/m 3x + 9y = 5 → 9y = -3x + 5 → y = (-3/9)x + 5/9 → y = -⅓x + 5/9 → its slope is -⅓ → perpendicular lines have slope m' = -1/(-⅓) = 3 → Every line perpendicular to 3x + 9y = 5 has slope 3.
Slope: 2/3 Point: (9, 11) Equation: 3y = 2x+15