Sure! Let's match the given equation to its graph by finding points on the line described by the equation [tex]\( y = \frac{3}{2} x - 6 \)[/tex].
1. Identify the equation and its slope-intercept form:
The equation given is [tex]\( y = \frac{3}{2} x - 6 \)[/tex]. This is in slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Here, the slope [tex]\( m = \frac{3}{2} \)[/tex] and the y-intercept [tex]\( b = -6 \)[/tex].
2. Find the coordinates of points on the line:
To match the line to its graph, let's find the y-values corresponding to specific x-values.
- For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = \frac{3}{2}(-1) - 6 = -\frac{3}{2} - 6 = -\frac{3}{2} - \frac{12}{2} = -\frac{15}{2} = -7.5
\][/tex]
So, the point is [tex]\( (-1, -7.5) \)[/tex].
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = \frac{3}{2}(0) - 6 = 0 - 6 = -6
\][/tex]
So, the point is [tex]\( (0, -6) \)[/tex].
3. Match the calculated points to the graph:
We now have two points on the line:
[tex]\[
(-1, -7.5) \text{ and } (0, -6)
\][/tex]
These coordinates lie on the line described by the equation [tex]\( y = \frac{3}{2} x - 6 \)[/tex].
In conclusion, the graph of the equation [tex]\( y = \frac{3}{2} x - 6 \)[/tex] will pass through the calculated points (-1, -7.5) and (0, -6).
