Ask a New Question
Menu

What is the equation of the line in standard form?



Responses

x−2y=4
x minus 2 y equals 4

x + 2y = 4
x + 2 y = 4

2x + y = 2
2 x + y = 2

2x−y=2
2 x minus y equals 2
A function graph of a line with two points (-1-4) and (2,2) with an x axis of negative five to five and a y axis of negative five to five

1 answer

To find the equation of the line in standard form that passes through the points \((-1, -4)\) and \((2, 2)\), we can follow these steps:

  1. Find the slope (m): We use the formula for the slope between two points, which is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \((x_1, y_1) = (-1, -4)\) and \((x_2, y_2) = (2, 2)\): \[ m = \frac{2 - (-4)}{2 - (-1)} = \frac{2 + 4}{2 + 1} = \frac{6}{3} = 2 \]

  2. Use the point-slope form: We can use the point-slope form of the equation, which is: \[ y - y_1 = m(x - x_1) \] Using the slope \(m = 2\) and the point \((2, 2)\): \[ y - 2 = 2(x - 2) \]

  3. Simplify to slope-intercept form: Distributing the right side: \[ y - 2 = 2x - 4 \] Adding 2 to both sides: \[ y = 2x - 2 \]

  4. Convert to standard form: We want to convert this to the standard form \(Ax + By = C\): \[ -2x + y = -2 \] To get the coefficients positive, multiply through by -1: \[ 2x - y = 2 \]

So, the equation of the line in standard form is: \[ \boxed{2x - y = 2} \]

This corresponds to one of the responses you provided:

2x - y = 2