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To solve question number 4 in the image:

We are given the equation of the line \( y = 5x - 3 \) that undergoes a translation by a vector \( T = \begin{pmatrix} a \\ 0 \end{pmatrix} \), resulting in the new line equation \( y = 5x - 18 \).

A translation affects only the constant term in the line equation because it represents a vertical shift in the graph. The slope (5) remains unchanged, and the translation moves the y-intercept.

The original equation is:
\[
y = 5x - 3
\]

After translation, it becomes:
\[
y = 5x - 18
\]

The translation by the vector \( T = \begin{pmatrix} a \\ 0 \end{pmatrix} \) shifts the y-intercept from -3 to -18.

The change in the y-intercept is \( -18 - (-3) = -15 \).

Thus, the value of \( a \) is the horizontal component of the translation that caused this change. Since the translation is vertical (along the y-axis), and the horizontal component doesn't affect the line, \( a = 15 \).

However, since there is a misinterpretation that \( a \) refers to a vertical shift, the correct value matching the options must be adjusted. From the choices provided, we check if

Diketahui garis y = 5x - 3 ditranslasikan oleh T = (a, 0) menghasilkan garis y = 5x - 18. Nilai a adalah ...

In this problem, the linear equation y = 5x - 3 is translated by the vector T = (a, 0), resulting in the new equation y = 5x - 18. Learn how to calculate the value of a, which affects the y-intercept in this transformation. This problem is suitable for students in Grades 9-10.

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