write an equation of the line that passes through the given points:
1.(-1,0),(0,-2)
m = y2 - y1 / x2 - x1
m = -2 - 0 / 0 - (-1)
m = -2/1
m = -2
point slope form
y - y1 = m (x - x1)
y - 0 = -2 (x - (-1))
y = -2 (x + 1)
y = -2x - 2
the slope of the line is:
(-2 - 0) /( 0 + 1) = -2
the slope of the line is also
(y-0)/(x+1) = slope from any point on the line to (-1,0)
so
y /(x+1) = -2
y = -2 x - 2
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now check
0 = -2 (-1) - 2 yes
-2 = -2(0) -2 yes so we got it.
To find the equation of the line that passes through two given points, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1),
where (x1, y1) represents one point on the line and m is the slope of the line.
Given the points (-1, 0) and (0, -2), let's find the slope first:
slope (m) = (change in y) / (change in x)
= (-2 - 0) / (0 - (-1))
= (-2) / (1)
= -2
Now that we have the slope, we can choose either of the two given points to substitute into the equation. Let's choose (-1, 0) as (x1, y1):
y - 0 = -2(x - (-1))
y = -2(x + 1)
Therefore, the equation of the line that passes through (-1, 0) and (0, -2) is y = -2(x + 1).