Write an equation of a line and identify the slope (-6,0) and (-3,10)
Answer (1)
The slope is 10/3.The equation is y = 10/3x + 20.We should determine the equation of the line.We'll start by identifying the slope.Apply the slope formula:[tex]\sf m=\cfrac{y_2-y_1}{x_2-x_1}[/tex]Substitute the values:[tex]\sf m=\cfrac{10-0}{-3-(-6)}[/tex][tex]\sf m=\cfrac{10}{-3+6}[/tex][tex]\sf m=\cfrac{10}{3}[/tex]Now we'll use the point-slope formula to help us write the equation of the line.Point-slope is:[tex]\sf y-y_1=m(x-x_1)[/tex]where:m = slope[tex]\sf (x_1,y_1)[/tex] is the first pointWe'll use (-6,0) for our point.Our slope is 10/3.So we plug in our values:[tex]\sf y-0=\cfrac{10}{3}(x-(-6)[/tex]Simplify:[tex]\sf y=\cfrac{10}{3}(x+6)[/tex]Distribute 10/3:[tex]\sf y=\cfrac{10}{3}x+\cfrac{10\times6}{3}[/tex][tex]\sf y=\cfrac{10}{3}x+\cfrac{60}{3}[/tex][tex]\sf y=\cfrac{10}{3}x+20[/tex]
