Question

1.) determine the equation of the line 4x+3y=12 in slope - intercept form, then determine the slope, the y - intercept, the x - intercept, and draw an accurate graph.

Explanation:

Step1: Convert to 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 start with the equation \(4x+3y = 12\).
Subtract \(4x\) from both sides: \(3y=-4x + 12\).
Divide each term by 3: \(y=-\frac{4}{3}x + 4\).

Step2: Identify slope and y - intercept

From the equation \(y =-\frac{4}{3}x + 4\), we can see that the slope \(m =-\frac{4}{3}\) and the y - intercept \(b = 4\). The y - intercept is the point where the line crosses the y - axis, so the point is \((0,4)\).

Step3: Find the x - intercept

The x - intercept is the point where \(y = 0\). Substitute \(y = 0\) into the original equation \(4x+3y=12\):
\(4x+3(0)=12\)
\(4x=12\)
Divide both sides by 4: \(x = 3\). So the x - intercept is the point \((3,0)\).

Step4: Graph the line

Plot the y - intercept \((0,4)\) and the x - intercept \((3,0)\) on the coordinate plane. Then draw a straight line through these two points.

Answer:

• Slope - intercept form: \(y =-\frac{4}{3}x + 4\)
• Slope: \(-\frac{4}{3}\)
• Y - intercept: \(4\) (point \((0,4)\))
• X - intercept: \(3\) (point \((3,0)\))
• To graph: Plot \((0,4)\) and \((3,0)\) and draw a line through them.