Answer:
[tex]\begin{cases}y=-5x+1\\y=5x-4 \end{cases}[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]\boxed{y=mx+b}[/tex]
where:
- m is the slope.
- b is the y-intercept (where the line crosses the y-axis).
Slope formula
[tex]\boxed{\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
Equation 1
Define two points on the line:
- [tex]\textsf{Let }(x_1,y_1)=(-1, 6)[/tex]
- [tex]\textsf{Let }(x_2,y_2)=(0, 1)[/tex]
Substitute the defined points into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-6}{0-(-1)}=-5[/tex]
From inspection of the graph, the line crosses the y-axis at y = 1 and so the y-intercept is 1.
Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:
[tex]y=-5x+1[/tex]
Equation 2
Define two points on the line:
- [tex]\textsf{Let }(x_1,y_1)=(1, 1)[/tex]
- [tex]\textsf{Let }(x_2,y_2)=(0, -4)[/tex]
Substitute the defined points into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-1}{0-1}=5[/tex]
From inspection of the graph, the line crosses the y-axis at y = -4 and so the y-intercept is -4.
Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:
[tex]y=5x-4[/tex]
Conclusion
Therefore, the system of linear equations shown by the graph is:
[tex]\begin{cases}y=-5x+1\\y=5x-4 \end{cases}[/tex]
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