Write the equation of a line that is perpendicular to the given line and that passes through the given point.
y - 4 = 5/2 (x + 3); (-7, 8)
the given line has slope 5/2
so, our new line will have slope -2/5
Now, we have a point and a slope, so using the point-slopr form, our new line is
y-8 = -2/5 (x+7)
Thank you so much!
To find the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line first. The given line has a slope of 5/2 because it is in slope-intercept form (y = mx + b) where the coefficient of x is the slope.
The slope of a line perpendicular to the given line is the negative reciprocal of the given line's slope. In this case, the slope of the perpendicular line is -2/5.
Now that we have the slope (-2/5) and a point that the perpendicular line passes through (-7, 8), we can use the point-slope form of a linear equation to find the equation of the perpendicular line.
The point-slope form is given by: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line, and m is the slope.
Substituting the values into the equation, we get:
y - 8 = -2/5(x - (-7))
Simplifying the equation:
y - 8 = -2/5(x + 7)
Distributing -2/5 to both terms in parentheses:
y - 8 = -2/5x - 2(2)
Simplifying further:
y - 8 = -2/5x - 14
Bringing the constant term to the right side:
y = -2/5x - 14 + 8
Simplifying again:
y = -2/5x - 6
Therefore, the equation of the line that is perpendicular to the given line and passes through the point (-7, 8) is y = -2/5x - 6.