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Masteriza [31]
3 years ago
7

What is the equation of the line that passes through point (4, 12) and has a intercept of -2​

Mathematics
1 answer:
kozerog [31]3 years ago
7 0

Answer:

\large\boxed{y=\dfrac{7}{2}x-2}

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept → (0, b)</em>

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have the point <em>(4, 12)</em>, and y-intercept <em>b = -2 → (0, -2)</em>.

Substitute:

m=\dfrac{-2-12}{0-4}=\dfrac{-14}{-4}=\dfrac{14:2}{4:2}=\dfrac{7}{2}

Finally:

y=\dfrac{7}{2}x-2

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The piece-wise linear functions can be written as follows:

  • f(x) = x, x \leq -2.
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<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

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  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For x equal or less than -2, the line passes through (-3,-3) and (-2,-2), hence the rule is:

f(x) = x, x \leq -2.

For x greater than -2 up to 1, the y-intercept is of -7, and the line also passes through (1,-8), hence the rule is:

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The rule is:

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When x = 2, y = -5, hence:

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Hence:

f(x) = 2x - 9, x > 1.

More can be learned about linear functions at brainly.com/question/24808124

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