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Sagot :
Answer:
Graph
[tex]y = -x+1[/tex] --- Slope intercept form
[tex]y +x= 1[/tex] --- Standard form
Points
[tex]y = 2x-2[/tex] --- Slope intercept form
[tex]y -2x=-2[/tex] --- Standard form
Step-by-step explanation:
Solving (a): The graph.
From the graph, we have:
[tex](x_1,y_1) = (1,0)[/tex]
[tex](x_2,y_2) = (0,1)[/tex]
First, calculate the slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{1 - 0}{0 - 1}[/tex]
[tex]m = \frac{1 }{- 1}[/tex]
[tex]m = -1[/tex]
The slope intercept equation is:
[tex]y = m(x-x_1)+y_1[/tex]
So, we have:
[tex]y = -1(x-1)+0[/tex]
[tex]y = -1(x-1)[/tex]
[tex]y = -x+1[/tex]
In standard form:
[tex]y = -x+1[/tex]
Add x to both sides
[tex]y +x= x-x+1[/tex]
[tex]y +x= 1[/tex]
Solving (b): The points
From the graph, we have:
[tex](x_1,y_1) = (0,-2)[/tex]
[tex](x_2,y_2) = (3,4)[/tex]
First, calculate the slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{4 - (-2)}{3 - 0}[/tex]
[tex]m = \frac{6}{3}[/tex]
[tex]m=2[/tex]
The slope intercept equation is:
[tex]y = m(x-x_1)+y_1[/tex]
So, we have:
[tex]y = 2(x-0)-2[/tex]
[tex]y = 2(x)-2[/tex]
[tex]y = 2x-2[/tex]
In standard form:
[tex]y = 2x-2[/tex]
Subtract 2x from both sides
[tex]y -2x= 2x-2x-2[/tex]
[tex]y -2x=-2[/tex]
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