Question

write an equation of the line passing through the given point and satisfying the given condition. give the equation (a) in slope - intercept form and (b) in standard form. (12, 3); perpendicular to 4x - y = 6 (a) write the equation of the line in slope - intercept form. $y = -\frac{1}{4}x + 6$ (simplify your answer. use integers or fractions for any numbers in the expression.) (b) write the equation of the line in standard form. (simplify your answer. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Recall standard form

The standard form of a linear equation is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\geq0\). We start with the slope - intercept form \(y=-\frac{1}{4}x + 6\).

Step2: Multiply by 4 to eliminate fraction

Multiply each term in the equation \(y=-\frac{1}{4}x + 6\) by 4 to get rid of the fraction.
\(4y=4\times(-\frac{1}{4}x)+4\times6\)
\(4y=-x + 24\)

Step3: Rearrange to standard form

Add \(x\) to both sides of the equation \(4y=-x + 24\) to get it in the form \(Ax+By = C\).
\(x + 4y=24\)

Answer:

\(x + 4y = 24\)