Which equation represents a line that passes through the points (7, 5) and (6, 1)?
m = (1-5) / (6-7) = -4/-1 = 4
y = 4 x + b
1 = 4*6 + b
b = -23
so
y = 4 x - 23
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check (6,1) ??
1 = 4*6 -23 yes
5 = 4*7 - 23 Yes whew !!!
Why did the line pass through the points (7, 5) and (6, 1)? Because it couldn't resist their magnetic attraction! But back to the equation, the slope between these two points can be calculated as (1 - 5) / (6 - 7), which simplifies to -4. Now we can use the point-slope form of a line and choose one of the given points, like (7, 5). So our equation is y - 5 = -4(x - 7). Let's simplify that: y - 5 = -4x + 28. And voilà! The equation is y = -4x + 33.
To find the equation of a line passing through two points, you can use the point-slope form of the equation, which is:
(y - y₁) = m(x - x₁)
Given points: (7, 5) and (6, 1)
First, find the slope (m) using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
m = (1 - 5) / (6 - 7)
m = -4 / -1
m = 4
Now, choose one of the points (let's choose (7, 5)), and substitute the values into the point-slope equation:
(y - y₁) = m(x - x₁)
(y - 5) = 4(x - 7)
Simplifying, we get:
y - 5 = 4x - 28
Rearranging the equation in slope-intercept form (y = mx + b), we get:
y = 4x - 23
So, the equation of the line passing through (7, 5) and (6, 1) is y = 4x - 23.
To find the equation of a line that passes through two given points, we can use the slope-intercept form of the equation of a line: y = mx + b, where m is the slope of the line and b is the y-intercept.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Given the points (7, 5) and (6, 1):
x1 = 7, y1 = 5
x2 = 6, y2 = 1
m = (1 - 5) / (6 - 7)
m = -4 / -1
m = 4
Now that we have the slope, we can use one of the points (x1, y1) and the slope (m) to find the value of b (the y-intercept).
Using the point (7, 5):
y = mx + b
5 = 4(7) + b
5 = 28 + b
b = 5 - 28
b = -23
So, the equation of the line that passes through the points (7, 5) and (6, 1) is:
y = 4x - 23