Find an equation of the line that satisfies the given conditions through (1,1) parallel to the line y=5x-8
To find the equation of a line that is parallel to the line y = 5x - 8 and passes through the point (1, 1), we can use the point-slope form of a linear equation.
The point-slope form is given by: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope of the line.
We know that the given line has a slope of 5 (since it is in the form y = mx + b), and since our desired line is parallel, it will also have a slope of 5.
Using the point-slope form with (x₁, y₁) = (1, 1) and m = 5, we can substitute these values into the equation:
y - 1 = 5(x - 1)
Simplifying:
y - 1 = 5x - 5
Adding 1 to both sides:
y = 5x - 5 + 1
y = 5x - 4
Therefore, the equation of the line that is parallel to y = 5x - 8 and passes through (1, 1) is y = 5x - 4.
The equation of a line parallel to another line has the same slope.
Given the equation y = 5x - 8, we can see that the slope is 5.
To find the equation of a line with slope 5 that passes through the point (1,1), we can use the point-slope form of a linear equation.
The point-slope form is given by: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
Using the point (1, 1) and slope 5, we can write:
y - 1 = 5(x - 1)
Now, let's simplify the equation:
y - 1 = 5x - 5
Add 1 to both sides:
y = 5x - 4
Therefore, the equation of the line that passes through (1,1) and is parallel to y = 5x - 8 is y = 5x - 4.