Write the equation of the line that passes through the points left bracket, 1, comma, minus, 4, right bracket(1,−4) and left bracket, 5, comma, minus, 1, right bracket(5,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
To find the equation of a line that passes through two given points, we can use the point-slope form.
The equation for point-slope form is: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line.
Let's calculate the slope (m) first:
m = (y₂ - y₁) / (x₂ - x₁)
m = (-1 - (-4)) / (5 - 1)
m = 3/4
Now, we can choose either one of the given points, let's use (1, -4).
Substituting the values in the point-slope form equation:
y - (-4) = (3/4)(x - 1)
Simplifying the equation further:
y + 4 = (3/4)(x - 1)
So, the equation of the line that passes through the two given points is:
y + 4 = (3/4)(x - 1)