Question

graph this line:
y - 1 = \frac{7}{4}(x + 5)

Explanation:

Step1: Identify the form of the equation

The given equation \( y - 1=\frac{7}{4}(x + 5) \) 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 our equation, \( x_1=- 5 \), \( y_1 = 1 \) and the slope \( m=\frac{7}{4} \).

Step2: Find a point on the line

Using the point - slope form, we know that the point \( (-5,1) \) lies on the line. To find another point, we can use the slope. The slope \( m=\frac{7}{4}=\frac{\text{rise}}{\text{run}} \). Starting from the point \( (-5,1) \), we move up (rise) 7 units and then move to the right (run) 4 units. So, the new \( x \) - coordinate is \( - 5+4=-1 \) and the new \( y \) - coordinate is \( 1 + 7=8 \). So, the point \( (-1,8) \) also lies on the line.

Step3: Plot the points and draw the line

First, plot the point \( (-5,1) \) on the coordinate plane. Then plot the point \( (-1,8) \). After that, draw a straight line passing through these two points.

Answer:

To graph the line \( y - 1=\frac{7}{4}(x + 5) \):

1. Identify the point \( (-5,1) \) from the point - slope form.
2. Use the slope \( \frac{7}{4} \) to find another point (e.g., from \( (-5,1) \), move 7 units up and 4 units right to get \( (-1,8) \)).
3. Plot the points \( (-5,1) \) and \( (-1,8) \) and draw a straight line through them.