Question

write the equation of the line described below in slope - intercept form. find the equation of the line that is perpendicular to the line y = 4x - 3 and passes through the point (-10,1). show your work here

Explanation:

Step1: Find the slope of the perpendicular line

The slope of the given line $y = 4x-3$ is $m_1 = 4$. For two perpendicular lines with slopes $m_1$ and $m_2$, $m_1\times m_2=- 1$. So, $4\times m_2=-1$, then $m_2 =-\frac{1}{4}$.

Step2: Use the point - slope form to find the equation

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-10,1)$ and $m =-\frac{1}{4}$. Substitute these values: $y - 1=-\frac{1}{4}(x + 10)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y-1=-\frac{1}{4}x-\frac{10}{4}$. Then add 1 to both sides: $y=-\frac{1}{4}x-\frac{5}{2}+1$. Simplify to get $y =-\frac{1}{4}x-\frac{3}{2}$.

Answer:

$y =-\frac{1}{4}x-\frac{3}{2}$