Question

graph the line.
$y - 4 = 5(x - 3)$

Explanation:

Step1: Identify the form of the equation

The given equation is \( y - 4 = 5(x - 3) \), which is in point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(3,4) \) and the slope \( m = 5 \).

Step2: Plot the point

First, plot the point \( (3,4) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m = 5=\frac{5}{1} \), which means for a run of \( 1 \) (increase in \( x \) by \( 1 \)), the rise is \( 5 \) (increase in \( y \) by \( 5 \)). Starting from \( (3,4) \), if we move \( 1 \) unit to the right (increase \( x \) by \( 1 \), so \( x=3 + 1=4 \)) and \( 5 \) units up (increase \( y \) by \( 5 \), so \( y = 4+5 = 9 \)), we get the point \( (4,9) \). We can also move in the opposite direction: for a run of \( - 1 \) (decrease \( x \) by \( 1 \), \( x = 3-1 = 2 \)) and a rise of \( - 5 \) (decrease \( y \) by \( 5 \), \( y=4 - 5=-1 \)), we get the point \( (2,-1) \).

Step4: Draw the line

Draw a straight line passing through the plotted points (such as \( (3,4) \), \( (4,9) \) or \( (3,4) \), \( (2,-1) \)) to represent the line \( y - 4 = 5(x - 3) \).

Answer:

To graph the line \( y - 4 = 5(x - 3) \), plot the point \( (3,4) \) and then use the slope \( 5 \) to find another point (e.g., \( (4,9) \) or \( (2,-1) \)) and draw a straight line through these points.