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The question asks for the equation of a line that passes through point \( K(3,2) \) and is perpendicular to the line \( y = -4x + 14 \). We are to find the value of \( x + y \).

Let's break down the problem step by step:

### Step 1: Equation of a line perpendicular to \( y = -4x + 14 \)
The slope of the line given by \( y = -4x + 14 \) is \( -4 \).

For a line to be perpendicular to this, its slope must be the negative reciprocal of \( -4 \), which is \( \frac{1}{4} \).

### Step 2: Equation of the new line
We know the slope of the new line is \( \frac{1}{4} \) and that it passes through the point \( K(3, 2) \). We use the point-slope form of the equation of a line:

\[
y - y_1 = m(x - x_1)
\]

where \( m = \frac{1}{4} \), \( x_1 = 3 \), and \( y_1 = 2 \).

\[
y - 2 = \frac{1}{4}(x - 3)
\]

Simplifying:

\[
y - 2 = \frac{1}{4}x - \frac{3}{4}
\]

\[
y = \frac{1}{4}x - \frac{3}{4} + 2
\]

\[
y = \frac{1}{4}x + \frac{5}{4}
\]

### Step 3: Solve for the point \( L(x, y) \)
The question states that \( L(x, y) \) and \( M(2,1) \) lie on the line. From this, we substitute \( x = 2 \) and \( y = 1 \) to check if point \( M(2,1) \) satisfies the equation:

\[
1 = \frac{1}{4}(2) + \frac{5}{4}
\]

\[
1 = \frac{2}{4} + \frac{5}{4}
\]

\[
1 = \frac{7}{4}
\]

Since this is not true, point \( M(2,1) \) does not lie on the line. Therefore, we must have a different setup for the line involving these conditions, or approach the next method for determining the intercept properly.

Let me know if you need additional steps clarified

Jika K(3,2), L(x,y), dan M(2,1), maka persamaan garis yang melalui titik K dan tegak lurus garis LM adalah y=-4x+14. Nilai dari x+y?

Learn how to find the value of x+y for a line passing through point K(3,2) and perpendicular to y=-4x+14. This problem covers key mathematical concepts such as linear equations, perpendicular lines, and point-slope form, suitable for Grades 9-12.

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