Question

1. write the equation in slope-intercept form for a line that passes through the point (3,5) and has a slope of 2. afterward, check if the point (6,12) lies on the line.

Explanation:

Step1: Recall slope-intercept form

Slope-intercept form: $y = mx + b$, where $m=2$, $(x,y)=(3,5)$

Step2: Solve for b

Substitute values: $5 = 2(3) + b$ → $5 = 6 + b$ → $b = -1$

Step3: Write the equation

$y = 2x - 1$

Step4: Check point (6,12)

Substitute $x=6$: $y = 2(6) - 1 = 11 ≠ 12$

Answer:

The equation is $y = 2x - 1$; the point (6,12) does not lie on the line.