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A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (0, 4) and (1, 1) The second line is labeled y - g(x) and is horizontal passing through (negative 2, 2), (0, 2), and (2, 2). The lines intersect at a point that is slightly to the right of (0.5, 2).
If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.

x =

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Flamecaster

Answer:

x=2/3

Step-by-step explanation:

Most of that information is unnecessary. Just plug in the values of f(x) and g(x) into the equation where they are equal to each other and solve.

-3x+4=2

-3x=-2

3x=2

x=2/3

abidemiokin

The value of x if both lines intersect is 2/3

Given the equation of a line that passed through the points (0, 4) and (1, 1) expressed as h(x) = -3x +4

The equation of the second line g(x) passing through the points (-2, 2) and (0, 2) is g(x) = 2

  • If the lines intersect, then h(x) = g(x)

Substituting the functions to get the value of "x"

[tex]-3x + 4 = 2[/tex]

Subtract 4 from both sides

[tex]-3x + 4 - 4 =2 - 4\\-3x = -2\\[/tex]

Divide both sides by - 3

[tex]\frac{-3x}{-3} =\frac{-2}{-3} \\x=\frac{2}{3}[/tex]

Hence the value of x if both lines intersect is 2/3

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