Question

Can someone show me how to write the standard form of the line that contains a slope of 2/3 and passes through the point (1, 1)?

Answer 1

`\large\boxed{y=(2)/(3)x+(1)/(3)\qquad\text{slope-intercept form}}\\\\\boxed{y-1=(2)/(3)x-(2)/(3)\qquad\text{point-slope form}}\\\\\boxed{2x-3y=-1\qquad\text{standard form}}`

Explanation:

`\text{The standard form:}\ Ax+By=C`

`\text{The point-slope form:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\\\\text{We have the slope}\ m=(2)/(3)\ \text{and the point}\ (1,\ 1).\ \text{Substitute:}\\\\\underline{y-1=(2)/(3)(x-1)}\qquad\text{use the distributive property}\\\\y-1=(2)/(3)x-(2)/(3)\qquad\text{add 1 to both sides}\\\\\underline{y=(2)/(3)x+(1)/(3)}`

`y=(2)/(3)x+(1)/(3)\qquad\text{multiply both sides by 3}\\\\3y=2x+1\qquad\text{subtract 2x from both sides}\\\\-2x+3y=1\qquad\text{change the signs}\\\\\underline{2x-3y=-1}`