Question

Write the slope intercept form of the equation of the line described

through (-4,-5) perpendicular to y=-2x+5
steps please but not too long though

Answer 1

• y=-2x+5

Compare to slope intercept form y=mx+b

• Slope=m=-2

Slope of the Perpendicular line 1/2

• Passing through (-4,-5)

Equation in point slope form

`\\ \rm\rightarrowtail y+5=1/2(x+4)`

`\\ \rm\rightarrowtail y=1/2x+2-5`

`\\ \rm\rightarrowtail y=1/2x-3`

Answer 2

`\sf y=\frac12x-3`

Explanation:

If two lines are perpendicular, the product of their slopes is -1.

The slope of the given equation is -2, so the slope of the line perpendicular to it is
`\sf \frac12` as
`\sf -2 * \frac12=-1`

Point-slope formula:
`\sf y-y_1=m(x-x_1)`

(where m is the slope and
`\sf (x_1,y_1)` is a point on the line)

Given:

• 
  `\sf m=\frac12`

• 
  `\sf (x_1,y_1)=(-4,-5)`

Substitute the given values into the formula:

`\sf \implies y-(-5)=\frac12(x-(-4))`

`\sf \implies y+5=\frac12x+2`

`\sf \implies y=\frac12x-3`