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For each part, write the equation that represents the line in slope-intercept form (y = mx + b) and standard form (ax + by = c where a, b, and c are integers and a is not negative).

For each part write the equation that represents the line in slopeintercept form y mx b and standard form ax by c where a b and c are integers and a is not nega class=

Respuesta :

MrRoyal

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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