[tex]\text{y = -x - 4}[/tex]Explanation:
Given equation:
[tex]\text{y = -x + 1}[/tex]
For two lines to be parallel, the slope of one will be the same as the slope of the second line
[tex]\begin{gathered} u\sin g\text{ equation of line:} \\ y\text{ = mx + b} \\ m\text{ = slope, b = y-intercept} \end{gathered}[/tex]
comparing the given equation with the equation of line:
[tex]\begin{gathered} y\text{ = y} \\ mx\text{ = -x = -1(x)} \\ m\text{ = -1} \\ b\text{ = 1} \end{gathered}[/tex]
This means the slope of the 1st line is -1. The slope of the second line will also be -1 since they are parallel
To get the y-intercept of the second line, we would insert the slope and the point given:
point given: (-7, 3) = (x, y)
[tex]\begin{gathered} y\text{ = mx + b} \\ 3\text{ = -1(-7) + b} \\ 3\text{ = 7 + b} \\ 3\text{ - 7 = b} \\ b\text{ = -4} \\ y-\text{intercept of 2nd line = -4} \end{gathered}[/tex]
The second equation is the equation of line that is parallel to the line y = -x + 1 and passes through (-7, 3)
Second equation:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = -1(x) + (-4)} \\ y\text{ = -x - 4} \end{gathered}[/tex][tex]\begin{gathered} In\text{ slope intercept form:} \\ y\text{ = -x - 4} \end{gathered}[/tex]
