# Write an equation in standard form Ax=By=C of the line that satisfies the given conditions. Use integer values for A, B, and C. passes through (2, 8) and (-4, 16)

Question
Equations
Write an equation in standard form $$Ax=By=C$$ of the line that satisfies the given conditions. Use integer values for A, B, and C. passes through (2, 8) and (-4, 16)

2021-02-12
Find the slope.
$$m = \frac{16-8}{-4-2}=\frac{8}{-6}=\frac{-4}{3}$$
Write the equation in point-slope form, simplify, then rewrite in standard form.
$$y-8=\frac{-4}{3}(x-2)$$
Simplify
$$y-8=\frac{-4}{3x}+\frac{8}{3}$$
Simplify
$$y=\frac{-4}{3x}+\frac{32}{3}$$
Multiply both sides by 3 to put in standard form.
$$3y=-4x+32$$
Put in $$Ax + By = C$$ form
$$4x+3y=32$$

### Relevant Questions

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.
Passing through (3,-1) and perpendicular to the line whose equation is x-9y-5=0
Write an equation for the line in point-slope form and slope-intercept form.
For the equation (-1,2), $$y= \frac{1}{2}x - 3$$, write an equation in slope intercept form for the line that passes through the given point and is parallel to the graph of the given equation.

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.
Passing through (-2,-8) and parallel to the line whose equation is $$y=-3x+4$$
Write an equation for the line in point-slope form and slope-intercept form.

Find an equation for the plane that
(a) is perpendicular to $$v=(1,1,1)$$ and passes through (1,0,0).
(b) is perpendicular to $$v=(1,2,3)$$ and passes through (1,1,1)
(c) is perpendicular to the line $$l(t)=(5,0,2)t+(3,-1,1)$$ and passes through (5,-1,0)
(d) is perpendicular to the line $$l(t)=(-1,-2,3)t+(0,7,1)$$ and passes through (2,4,-1).
For the equation, a. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation.
$$4/(x + 5) + 2/(x - 5) = 32/(x^{2} - 25)$$
Find values of a and b such that the system of linear equations has no solution.
x+2y=3
ax+by=-9
An equation of the form ax + b = 0 is called a(n) ? equation or a(n) ? -degree equation.
Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P.
A. Let y=f(x) be the equation of C. Find f(x).
B. Find the slope at P of the tangent to C.
C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?
D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.
E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.
Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.