Use point-slope form to write the equation of a line that passes through the point left bracket, minus, 16, comma, minus, 14, right bracket
(
−
16
,
−
14
)
(−16,−14) with slope minus, start fraction, 7, divided by, 8, end fraction
−
7
8
−
8
7
.
The equation of a line in point-slope form 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.
Given that the point is (-16, -14) and the slope is -7/8, the equation of the line is:
y - (-14) = -7/8(x - (-16))
Simplifying,
y + 14 = -7/8(x + 16)
Multiplying through by 8 to eliminate the fraction,
8y + 112 = -7(x + 16)
Expanding,
8y + 112 = -7x - 112
Rearranging terms,
7x + 8y = -224
So, the equation of the line in point-slope form is 7x + 8y = -224.
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
Where (x1, y1) is the given point on the line and m is the slope.
Substituting the given values, we have:
y - (-14) = (-7/8)(x -(-16))
Simplifying:
y + 14 = (-7/8)(x + 16)
Now, we can rewrite the equation in a more standard form:
8(y + 14) = -7(x + 16)
Expanding:
8y + 112 = -7x - 112
Rearranging the equation:
7x + 8y = -224
So, the equation of the line in point-slope form is y + 14 = (-7/8)(x + 16) and in standard form is 7x + 8y = -224.
To write the equation of a line using the point-slope form, you need two pieces of information: the coordinates of a point on the line and the slope of the line.
Given that the point is (−16,−14) and the slope is −7/8, you can now use the point-slope form to write the equation of the line.
The point-slope form of a linear equation is:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of a point on the line and m is the slope.
So, substituting the values into the equation:
y - (-14) = (-7/8)(x - (-16))
Simplifying:
y + 14 = (-7/8)(x + 16)
To get the desired equation in standard form, you can multiply both sides of the equation by 8 to clear the fraction:
8(y + 14) = -7(x + 16)
Expanding:
8y + 112 = -7x - 112
Arranging the terms to get the standard form:
7x + 8y = -224
Therefore, the equation of the line that passes through the point (−16,−14) with a slope of −7/8 is 7x + 8y = -224.