Question

a. Rewrite the equation 5 x plus y minus 3 equals 0 in​ slope-intercept form.
b. Give the slope and​ y-intercept.
c. Use the slope and​ y-intercept to graph the linear function.
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Part 1
a. The​ slope-intercept form of the equation is
  
enter your response here.
​(Simplify your answer. Use integers or fractions for any numbers in the​ equation.)
Part 2
b. The slope of the equation of the line is
  
enter your response here and the​ y-intercept is
  
enter your response here.
​(Type integers or​ fractions.)
Part 3
c. Use the slope and​ y-intercept to graph the line.

Answer 1

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:

1. 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:

1. **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.

2. **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).

3. **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).