Question

write an equation in slope intercept form form for the line that passes through (-2,4) and is parallel to the graph of the line y=-x+6

Answer 1

y=-x+2

Step-by-step 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:

`\begin{gathered} y=-x+6 \\ \text{Slope,m}=-1 \end{gathered}`

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:

`y-y_1=m(x-x_1)`

Substitute the given points and slope:

`\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}`

The equation of the line in slope-intercept form is y=-x+2.