Write the equation of a line I’m STANDARD FORM that is perpendicular to y=-1/4-13 and passes through (1,7)
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.
To find the equation of a line that is perpendicular to y=-1/4x-13, we need to determine the slope of the given line first.
The equation of the given line is in slope-intercept form (y=mx+b), where m is the slope of the line.
Comparing the given equation to the slope-intercept form, we can see that the slope (m) of the line is -1/4.
Perpendicular lines have slopes that are negative reciprocals of each other. So, to find the slope of the perpendicular line, we need to take the negative reciprocal of -1/4.
The negative reciprocal of -1/4 is 4/1, or simply 4.
Since we now have the slope of the perpendicular line (4), and we also have a point that the line passes through, which is (1,7), we can use the point-slope formula to find the equation of the line.
The point-slope formula is:
y - y₁ = m(x - x₁)
Substituting the values:
y - 7 = 4(x - 1)
Expanding the equation:
y - 7 = 4x - 4
To write the equation in standard form, we rearrange the equation by bringing all the terms to one side:
4x - y = -7 + 4
Simplifying the expression:
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.