Answer:
y=-x+2
Explanation:
Definitions
• The slope-intercept form of the equation of a line is y=mx+b.
,• Two lines are parallel if they have the same slope.
Given the line:
[tex]\begin{gathered} y=-x+6 \\ \text{Slope,m}=-1 \end{gathered}[/tex]Therefore, a line parallel to y=-x+6 will also have a slope of -1.
Thus, we are to determine the equation of a line passing through (-2,4) with a slope of -1.
Using the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]Substitute the given points and slope:
[tex]\begin{gathered} y-4=-1(x-(-2)) \\ y-4=-1(x+2) \\ y-4=-x-2 \\ y=-x-2+4 \\ y=-x+2 \end{gathered}[/tex]The equation of the line in slope-intercept form is y=-x+2.
