Question

Find the equation of the line in standard form that passes through the following points. Simplify your answer.

a) y equals negative 2x plus 6.
b) y equals 2x minus 6.
c) y equals 4x plus 2.
d) y equals negative 4x minus 2.

Answer 1

To find the equation of a line in standard form that passes through a given point, we need to use the formula y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line. We can find the equations in standard form for the given lines using this formula.

Step-by-step explanation:

To find the equation of a line in standard form that passes through a given point, we need to use the formula y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.

For example, for y = -2x + 6, the slope is -2 and the point is (0, 6). Substituting these values into the formula, we get y - 6 = -2(x - 0), which simplifies to y - 6 = -2x. Rearranging the equation in standard form, we get 2x + y = 6.

Similarly, for y = 2x - 6, y = 4x + 2, and y = -4x - 2, we can find the equations in standard form as -2x + y = -6, -4x - y = -2, and 4x - y = -2, respectively.