Write an equation of the line passing through each of the following pairs of points.
(−10, 4), (2, −5)
Again Helen stop trying to get answers to you homework when you don't understand the concept
-anonymouse
find the slope ... then use point-slope to write the equation
what do you mean
To find the equation of a line passing through two points, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where (x1, y1) represents one point on the line, and m represents the slope.
Step 1: Find the slope (m)
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points: (−10, 4), (2, −5)
Let (x1, y1) = (−10, 4) and (x2, y2) = (2, −5)
m = (-5 - 4) / (2 - -10)
m = (-9) / (2 + 10)
m = -9 / 12
m = -3 / 4
Step 2: Use one of the points and the slope to write the equation
We will use the point (−10, 4) and the slope (-3/4) in the point-slope form:
y - y1 = m(x - x1)
y - 4 = (-3/4)(x - (-10))
y - 4 = (-3/4)(x + 10)
y - 4 = (-3/4)x - 30/4
y - 4 = (-3/4)x - 15/2
Step 3: Simplify the equation
To simplify the equation, we can multiply every term by 4 to get rid of the fractions:
4(y - 4) = 4((-3/4)x - 15/2)
4y - 16 = -3x - 30
4y = -3x - 14
Therefore, the equation of the line passing through the points (−10, 4) and (2, −5) is 4y = -3x - 14.
(-10, 4), (2, -5).
Y = mx + b.
m = (-5-4)/(2+10) = -3/4.
b = y - mx = 4 - (-3/4)(-10) = -3 1/2 = -7/2.