To solve the pair of linear equations graphically, let's analyze the given equations step-by-step.
Firstly, we have the pair of equations:
[tex]\[
\begin{array}{l}
y = -2x + 3 \\
y = -4x - 1
\end{array}
\][/tex]
We need to graph both equations and find their point of intersection. To graph a linear equation of the form [tex]\( y = mx + c \)[/tex], we need to identify the slope (m) and the y-intercept (c).
1. Graph the first equation [tex]\( y = -2x + 3 \)[/tex]:
- The equation is in slope-intercept form [tex]\( y = mx + c \)[/tex].
- The slope [tex]\( m \)[/tex] is [tex]\(-2\)[/tex], which means that for every unit increase in [tex]\( x \)[/tex], [tex]\( y \)[/tex] decreases by 2 units.
- The y-intercept [tex]\( c \)[/tex] is [tex]\(3\)[/tex]. This is the point where the line crosses the y-axis.
2. Graph the second equation [tex]\( y = -4x - 1 \)[/tex]:
- This equation is also in slope-intercept form [tex]\( y = mx + c \)[/tex].
- The slope [tex]\( m \)[/tex] is [tex]\(-4\)[/tex], meaning that for every unit increase in [tex]\( x \)[/tex], [tex]\( y \)[/tex] decreases by 4 units.
- The y-intercept [tex]\( c \)[/tex] is [tex]\(-1\)[/tex]. This is the point where the line crosses the y-axis.
Now, we need to graph both lines on the same coordinate plane and examine where they intersect.
Choosing the correct steps:
The correct explanation for the graphical solution involves:
- Graphing the first equation with slope [tex]\(-2\)[/tex] and y-intercept [tex]\(3\)[/tex].
- Graphing the second equation with slope [tex]\(-4\)[/tex] and y-intercept [tex]\(-1\)[/tex].
- Finding the point of intersection of the two lines.
Thus, the correct statement is:
Graph the first equation, which has slope [tex]\(=-2\)[/tex] and [tex]\(y\)[/tex]-intercept [tex]\(=3\)[/tex], graph the second equation, which has slope [tex]\(=-4\)[/tex] and [tex]\(y\)[/tex]-intercept [tex]\(-1\)[/tex], and find the point of intersection of the two lines.
Hence, the correct choice among the given options is:
Graph the first equation, which has slope [tex]\(=-2\)[/tex] and [tex]\(y\)[/tex]-intercept [tex]\(=3\)[/tex], graph the second equation, which has slope [tex]\(=-4\)[/tex] and [tex]\(y\)[/tex]-intercept [tex]\(=-1\)[/tex], and find the point of intersection of the two lines.
