Question

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

Answer 1

Answer:

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

Standard form:   $2x - y = 4$

2. Slope-intercept form:  $y = \dfrac12x - 1$

Standard form:             $x - 2y = 2$

3. Slope-intercept form:   $y = \dfrac45x + \dfrac{21}{5}$

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

Step-by-step 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:   $2x - y = 4$

$\textsf{2. as} \ \ m = \dfrac12: \ \ y = \dfrac12x + b$

    $\textsf{at} \ (4, 1): \ \ 1 = \dfrac12(4) + b$

    $\implies b = -1$

Slope-intercept form:  $y = \dfrac12x - 1$

Standard form:             $x - 2y = 2$

$\textsf{3. as} \ \ m = \dfrac45: \ \ y = \dfrac45x + b$

   $\textsf{at} \ (1,5): \ \ 5 = \dfrac45(1) + b$

   $\implies b = \dfrac{21}{5}$

Slope-intercept form:   $y = \dfrac45x + \dfrac{21}{5}$

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