Q:

Which equation represents a line that passes through (-2, 4) and has a slope71

Accepted Solution

A:
Step-by-step explanation:The point-slope of an equation of a line:[tex]y-y_1=m(x-x_1)[/tex]m - slopeWe have the slope m = 71 and the point (-2, 4).Substitute:[tex]y-4=71(x-(-2))\\\\\bold{y-4=71(x+2)}[/tex]The slope-intercept form of an equation of a line:[tex]y=mx+b[/tex]Convert:[tex]y-4=71(x+2)[/tex]         use the distributive property[tex]y-4=71x+142[/tex]         add 4 to both sides[tex]\bold{y=71x+146}[/tex]The standard form of an equation of a line:[tex]Ax+By=C[/tex]Convert:[tex]y=71x+146[/tex]            subtract 71x from both sides[tex]-71x+y=146[/tex]        change the signs[tex]\bold{71x-y=-146}[/tex]The general form of an equation of a line:[tex]Ax+By+C=0[/tex]Convert:[tex]71x-y=-146[/tex]           add 146 to both sides[tex]\bold{71x-y+146=0}[/tex]