Answered

Find the best solutions to your problems with the help of IDNLearn.com. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.

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=

Sagot :

MrRoyalidn

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]

We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.