I just don't get it.

I just don't get it. Lines t and w are parallele in the xy-plane. The equation of line is 4x + 7y = 14, and line w passes through (-3,8). What is the vaule of the y- intercept of line w?

The equation of line is

\( 4x + 7y = 14\\ t(x)=y_t=-\frac{4}{7}x+2\)

                        m          n

\(m_t=m_w=-\frac{4}{7}\)   parallels

\(P_w(-3;8)\)

\(m_w=\frac{y-y_1}{x-x_1}\\ -\frac{4}{7}=\frac{y-8}{x+3)}\)

\(f(w)=y_w=-\frac{4}{7}x-\frac{12}{7}+8\\ {\color{blue}y_w=-\frac{4}{7}x+6.\overline{285714}..}(+\frac{44}{7})\)

The vaule of the y- intercept of line w is \(6\frac{2}{7}=6.\overline{285714}..\)

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