Question

graph the line.
$y - 4 = 3(x + 1)$

Explanation:

Step1: Identify the form of the equation

The given equation is \( y - 4 = 3(x + 1) \), which is in the point - slope form \( y - y_1=m(x - x_1) \), where \( m \) is the slope and \( (x_1,y_1) \) is a point on the line. Here, \( m = 3 \) and the point \( (x_1,y_1)=(- 1,4) \).

Step2: Plot the point

Locate the point \( (-1,4) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m = 3=\frac{3}{1} \), which means for a run of \( 1 \) unit (moving \( 1 \) unit to the right along the \( x \) - axis), we have a rise of \( 3 \) units (moving \( 3 \) units up along the \( y \) - axis). Starting from the point \( (-1,4) \), if we move \( 1 \) unit to the right (to \( x=-1 + 1=0 \)) and \( 3 \) units up (to \( y = 4+3 = 7 \)), we get the point \( (0,7) \). We can also move in the opposite direction: for a run of \( - 1 \) (moving \( 1 \) unit to the left) and a rise of \( - 3 \) (moving \( 3 \) units down). Starting from \( (-1,4) \), moving \( 1 \) unit to the left (to \( x=-1-1=-2 \)) and \( 3 \) units down (to \( y = 4 - 3=1 \)), we get the point \( (-2,1) \).

Step4: Draw the line

Draw a straight line passing through the points (for example, \( (-1,4) \), \( (0,7) \), and \( (-2,1) \)) on the coordinate plane.

(Note: Since the problem is about graphing a line, the final answer is the graph of the line passing through the points found using the point - slope form. If we were to describe the key points: the line passes through \( (-1,4) \) and has a slope of \( 3 \), so we can plot the points and draw the line.)

Answer:

The line is graphed by first plotting the point \((-1,4)\) and then using the slope \(m = 3\) to find other points (such as \((0,7)\) and \((-2,1)\)) and drawing a straight line through them.