Intersections 62534

The equation of the linear function is: y = -3x + 4
(a) determine the intersections with the axes
sketch chart

b) for which x applies
f (x) = - 1

c) for which x applies
f (x) = 0

d) for which y applies
f (-1/2) = y

Correct answer:

x₀ =  1.3333
y₀ =  0
x₁ =  0
y₁ =  4
x₂ =  1.6667
x₃ =  1.3333
y₄ =  5.5

Step-by-step explanation:

$$\begin{gathered} y_0=0 \\ {y}_0=-3\cdot x_0+4 \\ 0=-3\cdot x_0+4 \\ 3x_0=4 \\ {x}_0=\frac{4}{3}=1.33333333 \\ {x}_0=\frac{4}{3}\doteq 1.333333=1.3333 \end{gathered}$$

$x_1=0$

$y_1=-3\cdot x_1+4=-3\cdot 0+4=4$

$$\begin{gathered} -1=-3\cdot x_2+4 \\ 3x_2=5 \\ {x}_2=\frac{5}{3}=1.66666667 \\ {x}_2=\frac{5}{3}\doteq 1.666667=1.6667 \end{gathered}$$

$$\begin{gathered} 0=-3\cdot x_3+4 \\ 3x_3=4 \\ {x}_3=\frac{4}{3}=1.33333333 \\ {x}_3=\frac{4}{3}\doteq 1.333333=1.3333 \end{gathered}$$

$y_4=-3\cdot (-1/2)+4=5.5$

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