Question

1. graph a line that goes through the point (-1, -3) and perpendicular to the given graph.

Explanation:

Step1: Find slope of given line

Pick two points on the given line, say \((- 4,2)\) and \((4,0)\). The slope \(m_1\) of the given line using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\) is \(m_1=\frac{0 - 2}{4+4}=-\frac{1}{4}\).

Step2: Find slope of perpendicular line

The slope \(m_2\) of a line perpendicular to a line with slope \(m_1\) satisfies \(m_1m_2=- 1\). So \(m_2 = 4\) since \(-\frac{1}{4}m_2=-1\).

Step3: Use point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(-1,-3)\) and \(m = 4\). Substituting gives \(y+3 = 4(x + 1)\), which simplifies to \(y=4x+1\).

Step4: Graph the line

To graph \(y = 4x+1\), first plot the y - intercept at the point \((0,1)\). Then, using the slope of 4 (rise 4, run 1), we can find other points on the line.

Answer:

Graph the line \(y = 4x+1\) which passes through \((-1,-3)\) and is perpendicular to the given line.