What is an equation of the line that passes through the points left bracket, 5, comma, minus, 4, right bracket
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5
,
−
4
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(5,−4) and left bracket, minus, 5, comma, 4, right bracket
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−
5
,
4
)
(−5,4)?
To find the equation of the line passing through the points (5, -4) and (-5, 4), we can use the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
First, we need to find the slope (m) of the line. The slope is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (5, -4) and (-5, 4), we can substitute the values in the formula:
m = (4 - (-4)) / (-5 - 5) = 8 / -10 = -4/5
Now we have the slope (m = -4/5). Next, we can choose any of the two points to substitute in the slope-intercept form to find the y-intercept (b). Let's use the first point (5, -4):
-4 = (-4/5)(5) + b
-4 = -4 + b
b = -4 + 4
b = 0
Now we have the slope (m = -4/5) and the y-intercept (b = 0), so we can write the equation of the line:
y = (-4/5)x + 0
Simplifying the equation, we get:
y = -4/5x
To find the equation of the line passing through the points (5, -4) and (-5, 4), you can use the formula for the slope-intercept form of a linear equation, which is y = mx + b.
1. First, find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the two points:
m = (4 - (-4)) / (-5 - 5)
m = 8 / -10
m = -4/5
2. Now that we have the slope (m), we can use one of the points, for example, (5, -4), and plug it into the equation y = mx + b to find the y-intercept (b).
Using the point (5, -4):
-4 = (-4/5)(5) + b
Simplifying:
-4 = -4 + b
b = -4 + 4
b = 0
3. Now we can write the equation of the line using the slope (m) and y-intercept (b):
y = (-4/5)x + 0
Simplifying:
y = (-4/5)x
Therefore, the equation of the line passing through the points (5, -4) and (-5, 4) is y = (-4/5)x.
To find the equation of a line that passes through two points, we can use the slope-intercept form of a linear equation, which is y = mx + b.
Step 1: Find the slope (m)
The slope (m) can be found using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the given points: (5, -4) and (-5, 4), we can substitute the coordinates into the formula:
m = (4 - (-4)) / (-5 - 5)
= (4 + 4) / (-10)
= 8 / -10
= -4 / 5
So the slope (m) is -4/5.
Step 2: Find the y-intercept (b)
To find the y-intercept (b), we can use one of the given points (5, -4) and substitute its coordinates into the slope-intercept form (y = mx + b):
-4 = (-4/5)(5) + b
Simplifying the equation:
-4 = -4 + b
To isolate b, we can add 4 to both sides:
0 = b
So the y-intercept (b) is 0.
Step 3: Write the equation
Now that we have the slope (m) and the y-intercept (b), we can write the equation in slope-intercept form (y = mx + b):
y = (-4/5)x + 0
Simplifying the equation, we get:
y = -4/5x
Therefore, the equation of the line that passes through the points (5, -4) and (-5, 4) is y = -4/5x.