Write the point-slope form of the equation of the line through the point (3, -5) with a slope of 6
The point-slope form of a linear equation is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a point on the line and m is the slope of the line.
In this case, the point (3, -5) is on the line and the slope is 6. Substituting these values into the formula, we get:
y - (-5) = 6(x - 3)
Simplifying, we have:
y + 5 = 6(x - 3)
This is the point-slope form of the equation of the line.
To find the point-slope form of the equation of a line, we need the coordinates of a point on the line and the slope of the line.
Given:
Point: (3, -5)
Slope: 6
The point-slope form of the equation of a line is:
y - y1 = m(x - x1)
Where:
m is the slope of the line
(x1, y1) are the coordinates of a point on the line
Plugging in the values:
y - (-5) = 6(x - 3)
Simplifying the equation further gives us the point-slope form:
y + 5 = 6(x - 3)
So, the point-slope form of the equation of the line through the point (3, -5) with a slope of 6 is y + 5 = 6(x - 3).
To find the equation of a line in point-slope form, you need the coordinates of a point on the line and the slope of the line.
Given the point (3, -5) and a slope of 6, we can use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope.
Substituting the values into the formula, we have:
y - (-5) = 6(x - 3)
Simplifying the equation:
y + 5 = 6(x - 3)
Now, we can distribute the 6:
y + 5 = 6x - 18
Finally, we can isolate y by subtracting 5 from both sides:
y = 6x - 18 - 5
Simplifying further:
y = 6x - 23
Therefore, the point-slope form of the equation of the line through the point (3, -5) with a slope of 6 is: y = 6x - 23.