The point slope form of the equation of the line that passes through (-4, -3) and (12, 1) is y-1=1/4(x-12) what is the standard formula equation for this line?

Accepted Solution

Answer:x - 4y = 8Step-by-step explanation:The point-slope form of an equation of a line:[tex]y-y_1=m(x-x_1)[/tex]m - slopeThe formula of a slope:[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]============================================We have the points (-4, -3) and (12, 1).Substitute:[tex]m=d\frac{1-(-3)}{12-(-4)}=\dfrac{4}{16}=\dfrac{1}{4}[/tex]Put the volume of a slope and the coordinates of the point (12, 1) to the equation of a line:[tex]y-1=\dfrac{1}{4}(x-12)[/tex]The standard formula of an equation of a line:[tex]Ax+By=C[/tex]Convert:[tex]y-1=\dfrac{1}{4}(x-12)[/tex]           multiply both sides by 4[tex]4y-4=x-12[/tex]             add 4 to both sides[tex]4y=x-8[/tex]             subtract x from both sides[tex]-x+4y=-8[/tex]         change the signs[tex]x-4y=8[/tex]