a. Rewrite the given equation 7 x plus 9 y minus 63 equals 0 ​slope-intercept form.

Question

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.)

Answer 1

To convert the equation \( 7x + 9y - 63 = 0 \) into slope-intercept form, we'll solve for \( y \) in terms of \( x \).

Part a:

1. Start with the equation: \[ 7x + 9y - 63 = 0 \]

2. Move \( 7x \) and \( -63 \) to the other side: \[ 9y = -7x + 63 \]

3. Divide every term by \( 9 \) to isolate \( y \): \[ y = -\frac{7}{9}x + 7 \]

So, the slope-intercept form of the equation is: \[ y = -\frac{7}{9}x + 7 \]

Part b:

• The slope (\( m \)) is \( -\frac{7}{9} \).
• The y-intercept (\( b \)) is \( 7 \).

Part c:

To graph the linear function, we can use the slope and y-intercept:

1. Start at the y-intercept: Plot the point \( (0, 7) \) on the graph.
2. Use the slope: From the point \( (0, 7) \), use the slope of \( -\frac{7}{9} \) to find another point. This means for every 9 units you move to the right (positive x-direction), move down 7 units (negative y-direction).
   • From \( (0, 7) \), move to \( (9, 0) \) (down 7 from \( 7 \) to \( 0 \)).
3. Plot the point \( (9, 0) \).
4. Draw a line through the points \( (0, 7) \) and \( (9, 0) \).

The graph will be a straight line descending from left to right, showing the negative slope.

If you have graph paper, you can plot these points and connect them with a straight line to visualize the linear function.