What is the equation of the line that passes through the point left bracket, 2, comma, 5, right bracket
(
2
,
5
)
(2,5) and has a slope of 5
5
5?
Answer
The equation of the line can be written in slope-intercept form, which is y = mx + b.
Here, m represents the slope and (2,5) represents a point on the line.
So, plugging in the given values, the equation becomes y = 5x + b.
To find the value of b, we can substitute the coordinates of the given point into the equation.
So, 5 = 5(2) + b.
Simplifying that, we get 5 = 10 + b.
To solve for b, we subtract 10 from both sides of the equation.
So, b = 5 - 10 = -5.
Therefore, the equation of the line is y = 5x - 5.
To find the equation of a line using a point and a slope, we use the point-slope form equation:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Given that the point is (2, 5) and the slope is 5, we can substitute the values into the equation:
y - 5 = 5(x - 2)
Now let's simplify the equation:
y - 5 = 5x - 10
Next, we can move -5 to the right side of the equation by adding 5 to both sides:
y = 5x - 10 + 5
Simplifying further:
y = 5x - 5
Therefore, the equation of the line is y = 5x - 5.
To find the equation of a line given a point and slope, you can use the point-slope form of a linear equation. The point-slope form is: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
In this case, the given point is (2, 5) and the slope is 5. Plugging these values into the point-slope form, we have:
y - 5 = 5(x - 2)
Now, we can simplify and rearrange the equation to get it in slope-intercept form (y = mx + b):
y - 5 = 5x - 10
Adding 5 to both sides:
y = 5x - 5
So, the equation of the line that passes through the point (2, 5) and has a slope of 5 is y = 5x - 5.