Absolutely, let's go through the steps to graph the equation [tex]\( y = 2x - 3 \)[/tex] and identify the coordinates that match the graph we will draw.
### Step-by-Step Solution:
1. Understand the Equation:
The equation of the line is [tex]\( y = 2x - 3 \)[/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]\( m \)[/tex] is 2, and the y-intercept [tex]\( b \)[/tex] is -3.
2. Calculate Points for the Graph:
To graph this line, we need a few points that satisfy this equation. Let's choose several values of [tex]\( x \)[/tex] and find the corresponding [tex]\( y \)[/tex]-values.
- When [tex]\( x = -2 \)[/tex]:
[tex]\[
y = 2(-2) - 3 = -4 - 3 = -7
\][/tex]
- When [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 2(0) - 3 = 0 - 3 = -3
\][/tex]
- When [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 2(2) - 3 = 4 - 3 = 1
\][/tex]
3. Plot the Points:
- The point corresponding to [tex]\( x = -2 \)[/tex] is [tex]\( (-2, -7) \)[/tex]
- The point corresponding to [tex]\( x = 0 \)[/tex] is [tex]\( (0, -3) \)[/tex]
- The point corresponding to [tex]\( x = 2 \)[/tex] is [tex]\( (2, 1) \)[/tex]
4. Draw the Line:
On a graph paper, plot the points [tex]\((-2, -7)\)[/tex], [tex]\((0, -3)\)[/tex], and [tex]\((2, 1)\)[/tex].
Draw a straight line passing through these points.
From the calculations, the points determined are:
- [tex]\((-2, -7)\)[/tex]
- [tex]\((0, -3)\)[/tex]
- [tex]\((2, 1)\)[/tex]
### Conclusion:
The solution involves plotting the given points [tex]\((-2, -7)\)[/tex], [tex]\((0, -3)\)[/tex], and [tex]\((2, 1)\)[/tex] to draw the line for the equation [tex]\( y = 2x - 3 \)[/tex]. Let's now compare this with the provided options. We see that the points above match these coordinates. Based on manual graphing, also compare visually.
So, you should select the graph that correctly includes these points.
