Question

Write the equation of each line in slope-intercept form given the slope and point

slope = 1/2 runs through (-4,-2)

Answer 1

Answer:
`\text{y} = (1)/(2)\text{x}`

Work Shown

`\text{y}-\text{y}_1 = \text{m}(\text{x}-\text{x}_1)\\\\\text{y}-(-2) = (1)/(2)(\text{x}-(-4))\\\\\text{y}+2 = (1)/(2)(\text{x}+4)\\\\\text{y} = (1)/(2)(\text{x}+4)-2\\\\`

`\text{y} = (1)/(2)\text{x}+(1)/(2)*4-2\\\\\text{y} = (1)/(2)\text{x}+2-2\\\\\text{y} = (1)/(2)\text{x}\\\\`

Compare this to the slope-intercept form template y = mx+b

m = 1/2 = slope

b = 0 = y intercept

Another point on this line is the origin (0,0)

Use a graphing tool like GeoGebra to help confirm the answer.

Answer 2

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

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given slope m =
`(1)/(2)` , then

y =
`(1)/(2)` x + c ← is the partial equation

to find c , substitute (- 4, - 2 ) for x and y in the partial equation

- 2 =
`(1)/(2)` (- 4) + c = - 2 + c ( add 2 to both sides )

0 = c

y =
`(1)/(2)` x ← equation of line