To address the problem step by step, we will convert the equation into slope-intercept form (y = mx + b), identify the slope and y-intercept, and finally describe how to graph it.
Part 1
We start with the equation: \[ 2x + y - 5 = 0 \]
To rewrite it in slope-intercept form (\(y = mx + b\)):
- Move \(2x\) and \(-5\) to the right side: \[ y = -2x + 5 \]
So, the slope-intercept form of the equation is: \[ y = -2x + 5 \]
Part 2
From the equation \(y = -2x + 5\):
- The slope (\(m\)) is \(-2\).
- The y-intercept (\(b\)) is \(5\).
Thus:
- The slope of the equation of the line is \(-2\).
- The y-intercept is \(5\).
Part 3
To graph the line using the slope and y-intercept:
- Start at the y-intercept (0, 5). Plot the point (0, 5) on the graph.
- The slope is \(-2\), which can be interpreted as \(-2/1\). This means from the y-intercept (0, 5), you move down 2 units (negative slope) and 1 unit to the right.
- From (0, 5), move down 2 to (1, 3) and plot the point.
- You can also repeat this process or go in the negative direction (which means moving up 2 for every 1 unit to the left) to find more points if needed.
By connecting these points with a straight line, you will have the graph of the linear function.
Summary of Answers
- Part 1: The slope-intercept form of the equation is \(y = -2x + 5\).
- Part 2: The slope is \(-2\) and the y-intercept is \(5\).