Question

question
use the drawing tools to form the correct answers on the grid.
graph these equations:
y = 3x - 5
y = (1/2)x + 5

Explanation:

Step1: Graph \( y = 3x - 5 \)

To graph a linear equation in slope - intercept form \( y=mx + b \) (where \( m \) is the slope and \( b \) is the y - intercept), for the equation \( y = 3x-5 \), the y - intercept \( b=- 5 \), so we start by plotting the point \( (0,-5) \) on the y - axis. The slope \( m = 3=\frac{3}{1} \), which means from the point \( (0,-5) \), we move 3 units up and 1 unit to the right to get the next point \( (1,-2) \), and we can continue this process to get more points or draw the line through the two points we have.

Step2: Graph \( y=\frac{1}{2}x + 5 \)

For the equation \( y=\frac{1}{2}x + 5 \), the y - intercept \( b = 5 \), so we plot the point \( (0,5) \) on the y - axis. The slope \( m=\frac{1}{2} \), which means from the point \( (0,5) \), we move 1 unit up and 2 units to the right (or 2 units down and 4 units to the left, etc.) to get the next point, for example, \( (2,6) \), and then draw the line through the points \( (0,5) \) and \( (2,6) \).

(Note: Since this is a graphing problem, the final answer would be the two lines drawn on the grid according to the above steps. However, as we are providing a textual description of the graphing process, the key is to identify the y - intercepts and slopes for each line and use them to plot the lines.)

Answer:

The line for \( y = 3x-5 \) passes through \( (0, - 5) \) and has a slope of 3. The line for \( y=\frac{1}{2}x + 5 \) passes through \( (0,5) \) and has a slope of \( \frac{1}{2} \). The two lines are drawn on the coordinate grid as per the slope - intercept form graphing method.