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Equations, graphs, Slopes and y-intercepts : application

Equations Graphs Slopes And Yintercepts Application class=

Sagot :

Fieryanswererftidn

Answer:

[tex]\sf y= \dfrac{1}{2}x-5[/tex]

Explanation:

  • coordinates taken: (0, -5), (6, -2)

slope:

[tex]\rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\rightarrow \sf \dfrac{-2--5}{6-0}[/tex]

[tex]\rightarrow \sf \dfrac{1}{2}[/tex]

equation in slope intercept form:

  • y = m(x) + b                          [ where "m is slope", "b is y-intercept" ]

[tex]\sf y= \dfrac{1}{2}x-5[/tex]

View image Fieryanswererft
Estheridn

Answer:

[tex]y=\frac{1}{2}x-5[/tex]

Step-by-step explanation:

Slope-intercept form: y = mx + b

m = slope

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

To find slope, we use points on the line.

Here, I will be suing (-6, -8) and (8, -1)

[tex]m=\frac{1-(-8)}{8-(-6)} \\\\m=\frac{-1+8}{8+6} \\\\m=\frac{7}{14}\\\\m=\frac{1}{2}[/tex]

[tex]y=mx+b[/tex]

[tex]y=\frac{1}{2} x+b\\[/tex]

Now, we use either of our points (-6, -8) OR (8, 1) to find b.

I will be using (8, -1):

[tex]y=\frac{1}{2}x+b\\\\-1=\frac{1}{2}(8)+b\\\\-1=4+b\\\\-4-4\\\\-5=b[/tex]

[tex]y=\frac{1}{2}x+b== > y=\frac{1}{2}x-5[/tex]

Check your answer manually: (-6, -8)

[tex]y=\frac{9}{14}x-\frac{29}{7}\\\\-8=\frac{9}{14}(-6)-\frac{29}{7}\\\\-8=\frac{9}{7}(-3)-\frac{29}{7}\\\\-8=-\frac{27}{7}-\frac{29}{7}\\\\-8=-\frac{56}{7}\\\\-8=-8[/tex]

This statement is correct.

*You can also view the attached graph to verify the answer, meaning that those two points should lie on the same line.*

Hope this helps!

View image Esther
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