Question

Graph the line for y-1=7(x - 2) on the coordinate plane

Answer 1

The point-slope form:

$y=y_1=m(x-x_1)\\\\(x_1,\ y_1)-point\\m-slope$

We have

$y-1=7(x-2)$

Therefore

the point = (2, 1)

the slope = 7

The slope $m=\dfrac{\Delta y}{\Delta x}=7\to\dfrac{\Delta y}{\Delta x}=\dfrac{7}{1}$

7 units up and 1 unit right.

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Other method.

$y-1=7(x-2)\qquad|\text{use distributive property}\\\\y-1=7x-14\qquad|+1\\\\y=7x-13$

It's the slope-intercept form.

for x = 0 → y = 7(0) - 13 = 0 - 13 = -13 → (0, 13)

for x = 2 → y = 7(2) - 13 = 14 - 13 = 1 → (2, 1)