To solve the given pair of linear equations graphically, follow these detailed steps:
1. Graph the first equation [tex]\( y = -2x + 3 \)[/tex]:
- Identify the slope and y-intercept of the equation. The equation is in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- For [tex]\( y = -2x + 3 \)[/tex]:
- The slope ([tex]\( m \)[/tex]) is [tex]\(-2\)[/tex].
- The y-intercept ([tex]\( b \)[/tex]) is [tex]\(3\)[/tex].
- Plot the y-intercept [tex]\( (0, 3) \)[/tex] on the graph.
- Use the slope [tex]\(-2\)[/tex] to plot another point. From the y-intercept, move down 2 units and 1 unit to the right (since the slope is [tex]\(\frac{-2}{1}\)[/tex]), to get another point [tex]\( (1, 1) \)[/tex].
- Draw a line through both points.
2. Graph the second equation [tex]\( y = -4x - 1 \)[/tex]:
- Identify the slope and y-intercept of the equation.
- For [tex]\( y = -4x - 1 \)[/tex]:
- The slope ([tex]\( m \)[/tex]) is [tex]\(-4\)[/tex].
- The y-intercept ([tex]\( b \)[/tex]) is [tex]\(-1\)[/tex].
- Plot the y-intercept [tex]\( (0, -1) \)[/tex] on the graph.
- Use the slope [tex]\(-4\)[/tex] to plot another point. From the y-intercept, move down 4 units and 1 unit to the right (since the slope is [tex]\(\frac{-4}{1}\)[/tex]), to get another point [tex]\( (1, -5) \)[/tex].
- Draw a line through both points.
3. Find the point of intersection:
- The point where the two lines cross is the solution to the system of equations. Graphically find and verify the exact coordinates of this intersection point.
By following these steps, you have graphically solved for the intersection point where the two lines meet. Therefore, the correct answer is:
Graph the first equation, which has slope [tex]\(-2\)[/tex] and y-intercept [tex]\(3\)[/tex], graph the second equation, which has slope [tex]\(-4\)[/tex] and y-intercept [tex]\(-1\)[/tex], and find the point of intersection of the two lines.
