Question

which is an equation of the line that passes through the point (1,4) and has a slope of 3?
$\bigcirc\\ y = 3x + 1$
$\bigcirc\\ y = \frac{1}{3}x + 4$
$\bigcirc\\ y = 3x + 4$
$\bigcirc\\ y = 3x - 1$

Explanation:

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $m=3$, $x_1=1$, $y_1=4$.
$y - 4 = 3(x - 1)$

Step2: Simplify to slope-intercept form

Expand and isolate $y$.
$y - 4 = 3x - 3$
$y = 3x - 3 + 4$
$y = 3x + 1$

Step3: Verify the solution

Substitute $x=1$ into $y=3x+1$: $y=3(1)+1=4$, which matches the given point.

Answer:

$y = 3x + 1$