a line passes through point (-8,4) and has a slope of 3/4

Question

write the equation in ax+by=c form for this line use integers for a,b,and c

Answer 1

Initially, you can write the equation of the line easily by using the point-slope form:

y - y₁ = m(x - x₁) where "m" is the slope and (x₁, y₁) is a point. So, since m = 3/4 and (x₁, y₁) = (-8, 4) then the equation of the line is y - 4 = 3/4(x - -8)

Now, use algebra to modify the form. First simplify then multiply it out to get:

y - 4 = 3/4(x - -8)

y - 4 = 3/4(x + 8)

y - 4 = 3/4x + 6 then add 4 to both sides:

y = 3/4x + 10 then multiply both sides by 4:

4y = 3x + 40 then subtract 4y from both sides:

0 = 3x - 4y + 40 then subtract 40 from both sides to get:

-40 = 3x - 4y and switch it around to get:

3x - 4y = -40 meaning A = 3, B = -4, and C = -40

Answer 2

Start with using point-slope form: y-y₁= m(x-x₁)

Input the points and the slope

y-4 = 3/4(x+8)

Simplify this to slope-intercept form

y = 3/4x+10

Multiply the entire equation by four to get rid of the fraction

4y = 3x+40

Subtract the 3x from both sides

4y - 3x = 40

Rearrange the formula to standard form

-3x + 4y = 40