write slope intercept equation for line passes through (6,1) and has the slope 5/6
To write the slope-intercept equation of a line, we need to use the formula:
y = mx + b
Where:
- m is the slope of the line
- b is the y-intercept of the line
Given that the line passes through the point (6, 1) and has a slope of 5/6, we can substitute these values into the equation:
1 = (5/6)(6) + b
To find the value of b, we can simplify the equation:
1 = 5/6 * 6 + b
1 = 5/6 * 6 + b
1 = 30/6 + b
1 = 5 + b
Now, subtract 5 from both sides of the equation:
1 - 5 = b
-4 = b
Therefore, the value of b is -4.
Now we can rewrite the equation with the slope-intercept form:
y = (5/6)x - 4
So, the slope-intercept equation of the line passing through the point (6, 1) and with the slope of 5/6 is y = (5/6)x - 4.
To write the slope-intercept equation of a line, you need the slope (m) and the coordinates of a point on the line (x, y). In this case, the point is (6, 1), and the slope is 5/6.
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
1. Plug in the given coordinates into the equation: y = mx + b
Our coordinate values are x = 6 and y = 1, so the equation becomes 1 = (5/6) * 6 + b.
2. Simplify the equation:
1 = 5/6 * 6 + b
1 = 5 + b
Subtract 5 from both sides of the equation.
1 - 5 = b
-4 = b
3. Now that we have found the value of b, substitute it back into the equation:
y = (5/6) * x - 4
Therefore, the slope-intercept equation for the line that passes through the point (6, 1) and has a slope of 5/6 is y = (5/6) * x - 4.
You know the equation must be
y = (5/6)x + b
but (6,1) lies on it, so
1 = (5/6)(6) + b
1 = 5+b
b=-4
y = (5/6)x - 4