Question

Write the equation in slope-intercept form then change it to standard form with integer coefficients.

(6,8),m=2

(4,1),m=-1/2

(1,5),m=4/5

Answer 1

1. Slope-intercept form:
`y = 2x - 4`

Standard form:
`2x - y = 4`

2. Slope-intercept form:
`y = \frac12x - 1`

Standard form:
`x - 2y = 2`

3. Slope-intercept form:
`y = \frac45x + (21)/(5)`

Standard form:
`4x -5y = - 21`

Explanation:

Slope intercept form:
`y = mx + b`

where:

• 
  `y` = y-coordinate
• 
  `m` = slope
• 
  `x` = x-coordinate
• 
  `b` = y-intercept

Standard form:
`Ax + By = C`

`\textsf{1. as} \ m=2: \ \ y = 2x + b`

`\textsf{at} \ (6, 8): \ \ 8 = 2(6) + b`

`\implies b = -4`

Slope-intercept form:
`y = 2x - 4`

Standard form:
`2x - y = 4`

`\textsf{2. as} \ \ m = \frac12: \ \ y = \frac12x + b`

`\textsf{at} \ (4, 1): \ \ 1 = \frac12(4) + b`

`\implies b = -1`

Slope-intercept form:
`y = \frac12x - 1`

Standard form:
`x - 2y = 2`

`\textsf{3. as} \ \ m = \frac45: \ \ y = \frac45x + b`

`\textsf{at} \ (1,5): \ \ 5 = \frac45(1) + b`

`\implies b = (21)/(5)`

Slope-intercept form:
`y = \frac45x + (21)/(5)`

Standard form:
`4x -5y = - 21`