Use point-slope form to write the equation of a line that passes through the point left bracket, minus, 7, comma, minus, 4, right bracket(−7,−4) with slope 10/7.
The point-slope form of a linear equation is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
In this case, the given point is (−7,−4) and the slope is 10/7.
Plugging these values into the point-slope form, we get:
y - (-4) = (10/7)(x - (-7))
Simplifying further:
y + 4 = (10/7)(x + 7)
Distributing 10/7 to both terms inside the parentheses:
y + 4 = (10/7)x + 10
Subtracting 4 from both sides to isolate y on one side of the equation:
y = (10/7)x + 6
Therefore, the equation of the line is y = (10/7)x + 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.
In this case, the given point is (-7, -4) and the slope is 10/7.
Substituting these values into the point-slope form equation, we get:
y - (-4) = 10/7(x - (-7))
Simplifying further:
y + 4 = 10/7(x + 7)
Now, if we want to write the equation in standard form (Ax + By = C), we can multiply both sides of the equation by 7 to get rid of the fraction:
7(y + 4) = 10(x + 7)
Expanding and simplifying:
7y + 28 = 10x + 70
Rearranging the equation:
10x - 7y = -42
Hence, the equation of the line in standard form is 10x - 7y = -42.
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. In this case, the given point is (-7, -4), and the slope is 10/7.
The point-slope form of a linear equation is given by:
y - y₁ = m(x - x₁)
Where (x₁, y₁) represents the coordinates of the point on the line, and 'm' represents the slope.
Substituting the given values into the equation, we get:
y - (-4) = (10/7)(x - (-7))
Simplifying further:
y + 4 = (10/7)(x + 7)
Now, you can distribute the (10/7) to both terms inside the parentheses:
y + 4 = (10/7)x + (10/7)(7)
The (10/7)(7) simplifies to 10:
y + 4 = (10/7)x + 10
Finally, to get the equation into slope-intercept form (y = mx + b), you can subtract 4 from both sides:
y = (10/7)x + 10 - 4
Simplifying further:
y = (10/7)x + 6
So, the equation of the line that passes through the point (-7, -4) with a slope of 10/7 is y = (10/7)x + 6.