write an equation in slope - intercept form for the line described. write the slope and y - intercept as…

write an equation in slope - intercept form for the line described. write the slope and y - intercept as improper fractions, if necessary. passes through $(-7,-4)$, perpendicular to $y=\frac{1}{2}x + 9$

write an equation in slope - intercept form for the line described. write the slope and y - intercept as improper fractions, if necessary. passes through $(-7,-4)$, perpendicular to $y=\frac{1}{2}x + 9$

Answer

Explanation:

Step1: Find the slope of the required line

The slope of the line (y = \frac{1}{2}x+9) is (m_1=\frac{1}{2}). If two lines are perpendicular, the product of their slopes is (- 1), i.e., (m_1\times m_2=-1). Let the slope of the required line be (m_2). Then (\frac{1}{2}\times m_2=-1), so (m_2=-2).

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

The point - slope form of a line is (y - y_1=m(x - x_1)), where ((x_1,y_1)=(-7,-4)) and (m=-2). Substitute these values into the formula: (y-(-4)=-2(x - (-7))). Simplify the equation: (y + 4=-2(x + 7)). Expand the right - hand side: (y+4=-2x-14). Subtract 4 from both sides to get the slope - intercept form (y=-2x-18).

Answer:

The equation of the line in slope - intercept form is (y=-2x - 18), where the slope (m=-2) and the (y) - intercept (b=-18).