Question

I need help on this saturday guys

Answer 1

The point-slope form:

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

m - slope

(x₁, y₁) - the point

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (5, 4) and (2, -2). Substitute:

$m=\dfrac{-2-4}{2-5}=\dfrac{-6}{-3}=2$

$y-4=2(x-5)$ - point-slope form

$y-4=2x-10$        add 4 to both sides

$y=2x-6$  - slope-intercept form

$y=2x-6$      subtract 2x from both sides

$-2x+y=-6$      change the signs

$2x-y=6$   - standard form

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From the table we have two points (1, 3) and (2, 7). SubstituteL

$m=\dfrac{7-3}{2-1}=\dfrac{4}{1}=4$

$y-3=4(x-1)$   - point-slope form

$y-3=4x-4$     add 3 to both sides

$y=4x-1$    - slope-intercept form

$y=4x-1$      subtract 4x from both sides

$-4x+y=-1$     change the signs

$4x-y=1$    - standard form