Rewrite the equation in standard form of the line that passes through the given points (-1, -4) and (1, 6).
To find the equation of the line in standard form that passes through the given points (-1, -4) and (1, 6), we first need to find the slope of the line.
The formula to find the slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is:
m = (y₂ - y₁)/(x₂ - x₁)
Plugging in the values from the given points, we have:
m = (6 - (-4))/(1 - (-1))
= (6 + 4) / (1 + 1)
= 10 / 2
= 5
The slope of the line passing through the given points is 5.
Now, we can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
Plugging in the values for (x₁, y₁) = (-1, -4) and m = 5, we have:
y - (-4) = 5(x - (-1))
y + 4 = 5(x + 1)
y + 4 = 5x + 5
y = 5x + 5 - 4
y = 5x + 1
The equation of the line passing through the given points in slope-intercept form is y = 5x + 1.
To rewrite it in standard form, we can rearrange the equation to bring all the variables to one side of the equation:
-5x + y = 1
Hence, the equation of the line in standard form that passes through the given points (-1, -4) and (1, 6) is -5x + y = 1.