To graph the line given by the equation [tex]\( y = -\frac{5}{6}x - 4 \)[/tex], we need to identify at least two points that lie on the line. Here’s a step-by-step approach to find these points and graph the line:
1. Identify the Slope and Y-intercept:
The given equation is in slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
- Slope ([tex]\( m \)[/tex]) = [tex]\( -\frac{5}{6} \)[/tex]
- Y-intercept ([tex]\( b \)[/tex]) = -4
2. Find the Y-intercept Point:
The y-intercept occurs when [tex]\( x = 0 \)[/tex]. Plugging [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = -\frac{5}{6} \cdot 0 - 4 = -4 \][/tex]
So, the first point is [tex]\( (0, -4) \)[/tex].
3. Find Another Point:
To find another point, choose a different value for [tex]\( x \)[/tex]. Let's choose [tex]\( x = 6 \)[/tex]:
[tex]\[
y = -\frac{5}{6} \cdot 6 - 4
\][/tex]
Simplifying the calculation:
[tex]\[
y = -5 - 4 = -9
\][/tex]
So, the second point is [tex]\( (6, -9) \)[/tex].
4. Plot the Points:
- Plot the first point [tex]\( (0, -4) \)[/tex] on the graph.
- Plot the second point [tex]\( (6, -9) \)[/tex] on the graph.
5. Draw the Line:
- Using the line tool, draw a straight line that passes through both points [tex]\( (0, -4) \)[/tex] and [tex]\( (6, -9) \)[/tex].
This line represents the equation [tex]\( y = -\frac{5}{6}x - 4 \)[/tex] accurately on the graph.
