Write the equation of the line that passes through the points (4,7) and (5,−7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
To find the equation of the line that passes through the points (4,7) and (5,-7), we can use the point-slope form of a linear equation.
The point-slope form is given by the equation:
y - y₁ = m(x - x₁)
Where (x₁, y₁) represents the coordinates of a point on the line, and m represents the slope of the line.
To find the slope, we can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates (4,7) and (5,-7), we have:
m = (-7 - 7) / (5 - 4)
= -14 / 1
= -14
So the slope, m, of the line is -14.
Now let's choose (4,7) as the point on the line. Plugging the values into the point-slope form equation:
y - 7 = -14(x - 4)
Expanding and simplifying, we have:
y - 7 = -14x + 56
Add 7 to both sides of the equation:
y = -14x + 63
The equation of the line that passes through the points (4,7) and (5,-7) is y = -14x + 63 in fully simplified point-slope form.