Question

Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line. slope =1/2; containing the point (-1,1)

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: State the slope-intercept form of the equation of a line

`\begin{gathered} y=mx+c \\ where\text{ m is the slope} \\ c\text{ is the y-intercept} \end{gathered}`

STEP 2: Write the given properties

`\begin{gathered} slope(m)=(1)/(2) \\ point=(x_1,y_1)=(-1,1) \end{gathered}`

STEP 3: state the formula for using a slope and a point to get the equation of a line

`(y-y_1)=m(x-x_1)`

STEP 4: Substitute the given values

`\begin{gathered} (y-1)=(1)/(2)(x-(-1)) \\ (y-1)=(1)/(2)(x+1) \\ y-1=(x+1)/(2) \\ Multiply\text{ through by 2} \\ 2(y-1)=x+1 \\ 2y-2=x+1 \\ 2y=x+1+2 \\ 2y=x+3 \\ y=(x+3)/(2) \\ y=(x)/(2)+(3)/(2) \\ y=(1)/(2)x+(3)/(2) \end{gathered}`

Hence, the slope-intercept form of the equation of the line with the properties is given as:

`y=(1)/(2)x+(3)/(2)`