For what value of x does f(x) = g(x) when f(x) = 4x - 10 and g(x) = 0.5x + 7.5

x=5

Step-by-step explanation:

4x - 10 = 0.5x + 7.5

-0.5x       -0.5x

3.5x - 10 = 7.5

       +10    +10

3.5x = 17.5

divide both sides by 3.5 and you get x=5

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form