Question

a line passes through the point (-5, 7) and has a slope of 1. write an equation in point-slope form for this line.

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation is given by \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope of the line.

Step2: Identify values of \(x_1\), \(y_1\) and \(m\)

We are given that the line passes through the point \((-5,7)\), so \(x_1=-5\) and \(y_1 = 7\). The slope \(m = 1\).

Step3: Substitute values into the formula

Substitute \(x_1=-5\), \(y_1 = 7\) and \(m = 1\) into the point - slope formula \(y - y_1=m(x - x_1)\). We get \(y - 7=1\times(x-(-5))\), which simplifies to \(y - 7=1(x + 5)\) or \(y - 7=(x + 5)\) (since \(1\times(x + 5)=x + 5\)).

Answer:

\(y - 7=(x + 5)\)