What is the equation of the line that passes through the point left bracket, 3, comma, 5, right bracket(3,5) and has a slope of 2?
The equation of a line can be represented in slope-intercept form, which is given by:
y = mx + b
where m is the slope and b is the y-intercept.
Given that the line passes through the point (3,5) and has a slope of 2, we can substitute these values into the equation.
5 = 2(3) + b
Simplifying the equation:
5 = 6 + b
Subtracting 6 from both sides:
-1 = b
Now we have the y-intercept (b = -1), we can write the equation of the line:
y = 2x - 1
To find the equation of a line with a given point and slope, you can use the point-slope form of a linear equation.
Point-slope form: y - y1 = m(x - x1)
In this case, the given point is (3, 5) and the slope is 2. Plugging these values into the point-slope form, the equation becomes:
y - 5 = 2(x - 3)
Now, we can simplify the equation:
y - 5 = 2x - 6
Moving the constant to the other side:
y = 2x - 6 + 5
Simplifying further:
y = 2x - 1
Therefore, the equation of the line that passes through the point (3, 5) and has a slope of 2 is y = 2x - 1.
To find the equation of a line that passes through a point and has a given slope, you can use the point-slope form of the linear equation which is:
y - y1 = m(x - x1)
Where (x1, y1) represents the given point, and m represents the slope.
In this case, the given point is (3, 5) and the slope is 2.
Substituting these values into the equation, we get:
y - 5 = 2(x - 3)
Now, we can simplify the equation:
y - 5 = 2x - 6
Next, we can isolate the y-term by adding 5 to both sides of the equation:
y = 2x - 6 + 5
Simplifying further:
y = 2x - 1
Therefore, the equation of the line that passes through the point (3, 5) and has a slope of 2 is y = 2x - 1.