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3 years ago

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A line includes the points (-1, -10) and (1, 0). What is its equation in slope-intercept form?

1 answer:

netineya [11]3 years ago

8 0

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

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

We have the points (-1, -10) and (1, 0). Substitute:

$m=\dfrac{0-(-10)}{1-(-1)}=\dfrac{10}{1+1}=\dfrac{10}{2}=5$

<h3>y = 5x + b</h3>

Put the coordinates of the point (1, 0) to the equation of line:

$0=5(1)+b$

$0=5+b$ <em>subtract 5 from both sides</em>

$-5=b\to b=-5$

<h3>Answer: y = 5x - 5</h3>

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3 years ago

Thank you so much!!!

vova2212 [387]

Answer:

$\fbox{\begin{minipage}{16em}Option D: y = (4/7)x + 8 is correct\end{minipage}}$

Step-by-step explanation:

(1) A typical form of equation of a line is:

$y = Mx + b$

with, $M$ is slope and $b$ is y-intercept.

(2) Another straight line has equation in form of:

$y = Nx + c$

with $N$ is slope and $c$ is y-intercept

(3) If these two lines are perpendicular, according to the property of two perpendicular lines on the two-dimensional plane, we have:

$M$ x $N$ = -1

(4) Transform the given equation of original line into typical form:

$7x + 4y = -24\\$

<=> $4y = -7x - 24$

<=> $y = (\frac{-7}{4})x - \frac{24}{4}$

<=> $y = (\frac{-7}{4})x - 6$

=> $M = \frac{-7}{4}$

=> $N = \frac{-1}{M} = \frac{-1}{\frac{-7}{4} } = \frac{-4}{-7} = \frac{4}{7}$

=> Option D: $y = (\frac{4}{7})x + 8$ is correct (Slope = $\frac{4}{7}$ )

Hope this helps!

:)

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