Answer:
A) [tex]y=\frac{4}{3}x+4[/tex]
Step-by-step explanation:
Write the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
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Substitute and calculate
[tex]Substitute:[/tex] [tex]x_1=-6\\ x_2=0\\ y_1=-4\\ y_2=4[/tex] [tex]into\ m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute
[tex]m=\frac{4-(-4)}{-(-6)}[/tex]
Determine the sign
[tex]m=\frac{4+4}{6}[/tex]
Calculate the sum or difference
[tex]m=\frac{8}{6}[/tex]
Cross out the common factor
[tex]m=\frac{4}{3}[/tex]
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Substitute and calculate
[tex]Substitute[/tex] [tex]m=\frac{4}{3}\\ x=-6\\ y=-4[/tex] [tex]into\ y=mx+b[/tex]
Substitute
[tex]-4=\frac{4}{3}\times(-6)+b[/tex]
Reduce the expression to the lowest term
[tex]-4=-4\times2+b[/tex]
Calculate the product or quotient
[tex]-4=-8+b[/tex]
Rearrange variables to the left side of the equation
[tex]-b=-8+4[/tex]
Calculate the sum or difference
[tex]-b=-4[/tex]
Divide both sides of the equation by the coefficient of variable
[tex]b=4[/tex]
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Substitute
[tex]Substitute[/tex] [tex]y=\frac{4}{3}x+4\\ m=\frac{4}{3}[/tex] [tex]into\ y=mx+b:[/tex]
[tex]y=\frac{4}{3}x+4[/tex]
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Rewrite the equation of the line
[tex]Rewrite\ y=\frac{4}{3}x+4\ in\ slope-intercept\ form:[/tex]
[tex]y=\frac{4x}{3}+4[/tex]
I hope this helps you
:)
