Question

Which equation is the equation of a line that passes through (-10. 3) and is perpendicular to `y=5x-7`?

Answer 1

`y=-1/5 x +1`

Explanation:

I assume there is a typo and the problem should be:

write the equation of a line that passes through `(-10,3)` and is perpendicular to `y=5x-7`.

The line `y=5x-7` is in slope-intercept form `y=mx+b` where `m` is the slope. The slope of this line is thus `m=5`.

Perpendicular lines have slopes which are negative reciprocals. In other words, take the reciprocal of the slope and change the sign.

The negative reciprocal of `5` is `-1/5`.

To find the equation of a line which passes through `(color(red)(-10),color(red)3)` and with a slope of `color(blue)m= color(blue)(-1/5)`, use the point- slope formula:

`y-color(red)(y_1)=color(blue)m(x-color(red)(x_1))` where `(color(red)(x_1),color(red)( y_1))` is a point and `color(blue)m` is the slope.

`y-color(red)(3)=color(blue)(-1/5)(x-color(red)(-10))`

`y-3=-1/5(x+10)color(white)(aaa)` Equation in point-slope form

To put the equation in slope-intercept form, distribute the `-1/5`.

`y-3=-1/5 x-2`

Add 3 to both sides.

`y-3=-1/5 x-2`
`color(white)a+3color(white)(aaaaaaaa)+3`

`y=-1/5 x +1`