Question

5
select the correct answer from each drop-down menu.
consider the given equation.
3x + 2y = 8
the equation y = x + represents the line parallel to the given equation and passes through the point (-2,5).
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Explanation:

Step1: Find slope of given line

Rewrite \(3x + 2y = 8\) in slope - intercept form (\(y=mx + b\), where \(m\) is slope).
Subtract \(3x\) from both sides: \(2y=-3x + 8\).
Divide by 2: \(y=-\frac{3}{2}x + 4\).
Parallel lines have equal slopes, so slope of new line \(m =-\frac{3}{2}\).

Step2: Use point - slope form to find equation

Point - slope form: \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(-2,5)\) and \(m =-\frac{3}{2}\).
Substitute: \(y - 5=-\frac{3}{2}(x + 2)\).
Expand: \(y - 5=-\frac{3}{2}x-3\).
Add 5 to both sides: \(y=-\frac{3}{2}x+2\).

Answer:

The first drop - down (coefficient of \(x\)) is \(-\frac{3}{2}\) and the second drop - down (constant term) is \(2\). So the equation is \(y =-\frac{3}{2}x + 2\).