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morpeh [17]
3 years ago
7

A line includes the points (-39,49) and (0,0). What is its equation in slope-intercept form?

Mathematics
1 answer:
malfutka [58]3 years ago
5 0

Answer:

The equation in the slope-intercept form will be:

y=-\frac{49}{39}x+0

Step-by-step explanation:

Given the points

  • (-39,49)
  • (0,0)

Finding the slope between the points using the formula

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(-39,\:49\right),\:\left(x_2,\:y_2\right)=\left(0,\:0\right)

m=\frac{0-49}{0-\left(-39\right)}

m=-\frac{49}{39}

We know that the point-slope of the line equation is

y-y_1=m\left(x-x_1\right)

substituting m=-\frac{49}{39} and (-39,49)  in the equation

y-y_1=m\left(x-x_1\right)

y-49=\frac{-49}{39}\left(x-\left(-39\right)\right)

Now writing the equation in slope-intercept form

y=mx+b

where m is the slope and b is the y-intercept

y-49=\frac{-49}{39}\left(x-\left(-39\right)\right)

y-49=\frac{-49}{39}\left(x+39\right)

\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}

y-49=-\frac{49}{39}\left(x+39\right)

\mathrm{Add\:}49\mathrm{\:to\:both\:sides}

y-49+49=-\frac{49}{39}\left(x+39\right)+49

y=-\frac{49}{39}x+0              ∵ y=mx+b

Where

m=-\frac{49}{39} and the y-intercept i.e. b=0

Therefore, the equation in the slope-intercept form will be:

y=-\frac{49}{39}x+0

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