Write the equation of a line I’m STANDARD FORM that is perpendicular to y=-1/4-13 and passes through (1,7)

1 answer

To find the equation of a line that is perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line.

The given line is y = -1/4x - 13. The slope of this line is -1/4.

The negative reciprocal of -1/4 is 4/1 or simply 4.

Now, we know that the slope of the line we are trying to determine is 4, and it passes through the point (1,7).

Using the point-slope form of a linear equation, we can write the equation of the line:

y - y₁ = m(x - x₁)

where m is the slope, and (x₁, y₁) is a point on the line.

Plugging in the values, we have:

y - 7 = 4(x - 1)

Expanding the equation, we get:

y - 7 = 4x - 4

To put the equation in standard form, we bring the variables and constants to one side of the equation:

4x - y = 7 - 4

Simplifying further:

4x - y = 3

Therefore, the equation of the line in standard form that is perpendicular to y = -1/4x - 13 and passes through (1,7) is 4x - y = 3.