Question

line l1 has the following equation: $4x + 3y = 15$
2a express the equation of l1 in slope - intercept form.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We need to solve the given equation \(4x + 3y=15\) for \(y\).

Step2: Isolate the \(y\) - term

Subtract \(4x\) from both sides of the equation \(4x + 3y = 15\).
We get \(3y=-4x + 15\).

Step3: Solve for \(y\)

Divide each term in the equation \(3y=-4x + 15\) by 3.
\(y=\frac{-4x + 15}{3}\), which can be rewritten as \(y=-\frac{4}{3}x + 5\).

Answer:

\(y = -\frac{4}{3}x+5\)