Question

Hello could you please help me with this question? Write an equation in standard form of the line that passes through (7,-3) and has a y-intercept of 2

Answer 1

Given

Point (x,y) = (7,-3)

y-intercept b = 2

Substitute the following values to the slope-intercept form

`\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}`
`\begin{gathered} (x,y)=(7,-3) \\ b=2 \\ \\ y=mx+b \\ -3=m(7)+2 \\ -3-2=7m \\ 7m=-5 \\ m=-(5)/(7) \end{gathered}`

Now that we have solved for the slope, the equation of the line in slope intercept form is

`\begin{gathered} y=-(5)/(7)x+2 \\ \\ \text{Multiply all the terms with 7 to get rid of the fractions} \\ 7\mleft[y=-(5)/(7)x+2\mright]7 \\ 7y=-5x+14 \end{gathered}`

Rearrange the equation so that it is in the standard form Ax + By = C

`\begin{gathered} 7y=-5x+14 \\ 5x+7y=-5x+5x+14 \\ 5x+7y=\cancel{-5x+5x}+14 \\ \\ \text{The standard form of the line that passes through }(7,-3)\text{ and has a y-intercept of 2} \\ 5x+7y=14 \end{gathered}`