Question

graph the line.
y = 2x - 5

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = 2x - 5 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 2 \) (which can be written as \( \frac{2}{1} \)) and \( b=- 5 \).

Step2: Plot the y - intercept

The y - intercept is \( b=-5 \), so we plot the point \( (0,-5) \) on the y - axis.

Step3: Use the slope to find another point

The slope \( m = \frac{2}{1} \) means that from the point \( (0,-5) \), we move up 2 units (since the numerator of the slope is 2) and then move 1 unit to the right (since the denominator of the slope is 1). This gives us the point \( (0 + 1,-5+2)=(1,-3) \). We can also move down 2 units and left 1 unit from \( (0,-5) \) to get another point, for example, \( (0 - 1,-5-2)=(-1,-7) \).

Step4: Draw the line

Draw a straight line through the points we have plotted (such as \( (0,-5) \), \( (1,-3) \)) to graph the line \( y = 2x-5 \).

(Note: Since the question is about graphing, the final answer is the graph of the line \( y = 2x - 5 \) passing through points like \( (0,-5) \), \( (1,-3) \), \( (2,-1) \), etc. But in text - based form, we can describe the process as above.)

Answer:

The line \( y = 2x - 5 \) is graphed by plotting the y - intercept \( (0,-5) \) and then using the slope \( 2 \) (rise 2, run 1) to find other points (e.g., \( (1,-3) \), \( (2,-1) \), \( (-1,-7) \)) and drawing a straight line through them.