Question

graph the line.
$y - 2 = \frac{3}{4}(x + 1)$

Explanation:

Step1: Identify the form of the equation

The given equation \( y - 2=\frac{3}{4}(x + 1) \) is in the point - slope form of a linear equation, which is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1) \) is a point on the line and \( m \) is the slope. In this case, \( x_1=- 1 \), \( y_1 = 2 \) and the slope \( m=\frac{3}{4} \).

Step2: Plot the point

First, plot the point \( (-1,2) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=\frac{3}{4} \) means that for every 4 units we move to the right (increase in \( x \) by 4), we move up 3 units (increase in \( y \) by 3). Starting from the point \( (-1,2) \), if we move 4 units to the right ( \( x=-1 + 4=3 \)) and 3 units up ( \( y = 2+3 = 5 \)), we get the point \( (3,5) \). We can also move in the opposite direction: from \( (-1,2) \), move 4 units to the left ( \( x=-1-4=-5 \)) and 3 units down ( \( y = 2 - 3=-1 \)) to get the point \( (-5,-1) \).

Step4: Draw the line

Draw a straight line through the points \( (-1,2) \), \( (3,5) \) (and/or \( (-5,-1) \)) to graph the line.

Answer:

To graph the line \( y - 2=\frac{3}{4}(x + 1) \), plot the point \((-1,2)\), then use the slope \(\frac{3}{4}\) to find other points (e.g., \((3,5)\) or \((-5,-1)\)) and draw a straight line through them.