Use point-slope form to write the equation of a line that passes through the point left bracket, minus, 13, comma, minus, 11, right bracket
(
−
13
,
−
11
)
(−13,−11) with slope minus, one fifth
−
1
5
−
5
1
y - (-11) = -1/5 (x - (-13))
y + 11 = -1/5 (x + 13)
To write the equation of a line using the point-slope form, we will use the formula:
y - y1 = m(x - x1)
where (x1, y1) is the given point (−13,−11) and m is the given slope (−1/5).
Substituting the values into the formula, we get:
y - (-11) = (-1/5)(x - (-13))
Simplifying, we have:
y + 11 = (-1/5)(x + 13)
Distributing the -1/5 to both terms inside the parentheses:
y + 11 = (-1/5)x - (1/5)(13)
Simplifying further:
y + 11 = (-1/5)x - 13/5
By isolating y on one side, we subtract 11 from both sides:
y = (-1/5)x - 13/5 - 11
Simplifying:
y = (-1/5)x - 13/5 - 55/5
Combining the fractional terms:
y = (-1/5)x - (13 + 55)/5
y = (-1/5)x - 68/5
Therefore, the equation of the line in point-slope form is:
y = (-1/5)x - 68/5
To write the equation of a line using point-slope form, you need to have the coordinates of a point on the line and the slope of the line.
The point given is (-13, -11), and the slope is -1/5.
The point-slope form of a linear equation is:
y - y₁ = m(x - x₁),
where (x₁, y₁) are the coordinates of the given point and m is the slope.
Plugging in the values into the formula, we have:
y - (-11) = -1/5(x - (-13)),
Simplifying the equation:
y + 11 = -1/5(x + 13),
Distributing -1/5:
y + 11 = (-1/5)x - 13/5,
To isolate y, subtract 11 from both sides:
y = (-1/5)x - 13/5 - 11,
Combining constants:
y = (-1/5)x - 13/5 - 55/5,
Finding a common denominator:
y = (-1/5)x - (13 + 55)/5,
Simplifying the equation:
y = (-1/5)x - 68/5.
So, the equation of the line passing through the point (-13, -11) with a slope of -1/5 is y = (-1/5)x - 68/5.