To solve the problem, we'll go through each part step by step.
Part 1
We need to rewrite the equation \( 5x + y - 3 = 0 \) in slope-intercept form. The slope-intercept form of a linear equation is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
Starting with the given equation:
- Rearrange the equation to isolate \( y \):
\[ y = -5x + 3 \]
Thus, the slope-intercept form of the equation is:
\[ \boxed{y = -5x + 3} \]
Part 2
From the equation \( y = -5x + 3 \):
- The slope \( m \) is \( -5 \).
- The y-intercept \( b \) is \( 3 \).
So, we can fill in:
- The slope of the equation of the line is \( \boxed{-5} \).
- The y-intercept is \( \boxed{3} \).
Part 3
To graph the linear function using the slope and y-intercept:
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Start at the y-intercept (0, 3): This point is where the line crosses the y-axis. Plot the point (0, 3) on the graph.
-
Use the slope (-5): The slope tells us how to rise over run. Here, the slope \( -5 \) can be interpreted as \( -5/1 \), which means for every 1 unit you move to the right (increase in x), you move down 5 units (decrease in y).
- From the point (0, 3), move 1 unit to the right (to x = 1), and then move down 5 units to y = -2. Mark this second point at (1, -2).
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Draw the line: Draw a straight line through the points (0, 3) and (1, -2), extending it in both directions.
This completes the graph of your linear function based on the slope and y-intercept.
In summary:
- The slope-intercept form is \( y = -5x + 3 \).
- The slope is \( -5 \) and the y-intercept is \( 3 \).
- The points used for graphing include (0, 3) and (1, -2).