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The points (–9,s) and (–6,–10) fall on a line with a slope of –4. What is the value of s?

Sagot :

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Step-by-step explanation:

We can set up an equation for this line using slope intercept form:

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

Where [tex]m[/tex] is the slope of the line and [tex]b[/tex] is the y-intercept (where the line cross the Y-axis at [tex]x = 0[/tex]).

We know that the slope of the line is [tex]-4[/tex] so we can plug that in for [tex]m[/tex], but we don't know [tex]b[/tex], so we'll have to use the given point [tex])(-6, -10)[/tex] to help solve for it:

[tex]y = -4x + b[/tex]

[tex]-10 = -4(-6) + b[/tex]

[tex]-10 = 24 + b[/tex]

[tex]b = -34[/tex]

This means the equation of the line is [tex]y = -4x - 34[/tex]. Now we can plug in the point [tex](-9, s)[/tex] and solve for [tex]s[/tex]:

[tex]y = -4x - 34[/tex]

[tex]s = -4(-9) - 34[/tex]

[tex]s = 36 - 34[/tex]

[tex]s = 2[/tex]

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