Answer:
1. Slope-intercept form: [tex]y = 2x - 4[/tex]
Standard form: [tex]2x - y = 4[/tex]
2. Slope-intercept form: [tex]y = \dfrac12x - 1[/tex]
Standard form: [tex]x - 2y = 2[/tex]
3. Slope-intercept form: [tex]y = \dfrac45x + \dfrac{21}{5}[/tex]
Standard form: [tex]4x -5y = - 21[/tex]
Step-by-step explanation:
Slope intercept form: [tex]y = mx + b[/tex]
where:
- [tex]y[/tex] = y-coordinate
- [tex]m[/tex] = slope
- [tex]x[/tex] = x-coordinate
- [tex]b[/tex] = y-intercept
Standard form: [tex]Ax + By = C[/tex]
[tex]\textsf{1. as} \ m=2: \ \ y = 2x + b[/tex]
[tex]\textsf{at} \ (6, 8): \ \ 8 = 2(6) + b[/tex]
[tex]\implies b = -4[/tex]
Slope-intercept form: [tex]y = 2x - 4[/tex]
Standard form: [tex]2x - y = 4[/tex]
[tex]\textsf{2. as} \ \ m = \dfrac12: \ \ y = \dfrac12x + b[/tex]
[tex]\textsf{at} \ (4, 1): \ \ 1 = \dfrac12(4) + b[/tex]
[tex]\implies b = -1[/tex]
Slope-intercept form: [tex]y = \dfrac12x - 1[/tex]
Standard form: [tex]x - 2y = 2[/tex]
[tex]\textsf{3. as} \ \ m = \dfrac45: \ \ y = \dfrac45x + b[/tex]
[tex]\textsf{at} \ (1,5): \ \ 5 = \dfrac45(1) + b[/tex]
[tex]\implies b = \dfrac{21}{5}[/tex]
Slope-intercept form: [tex]y = \dfrac45x + \dfrac{21}{5}[/tex]
Standard form: [tex]4x -5y = - 21[/tex]
