Question

Which equation represents a line that passes through (-2, 4) and has a slope
71

Answer 1

Explanation:

The point-slope of an equation of a line:

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

m - slope

We have the slope m = 71 and the point (-2, 4).

Substitute:

`y-4=71(x-(-2))\\\\\bold{y-4=71(x+2)}`

The slope-intercept form of an equation of a line:

`y=mx+b`

Convert:

`y-4=71(x+2)` use the distributive property

`y-4=71x+142` add 4 to both sides

`\bold{y=71x+146}`

The standard form of an equation of a line:

`Ax+By=C`

Convert:

`y=71x+146` subtract 71x from both sides

`-71x+y=146` change the signs

`\bold{71x-y=-146}`

The general form of an equation of a line:

`Ax+By+C=0`

Convert:

`71x-y=-146` add 146 to both sides

`\bold{71x-y+146=0}`