Question

question
what is the equation of the line that passes through the point (1,4) and has a slope of 4?

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is given by $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $x_1 = 1$, $y_1=4$ and $m = 4$.

Step2: Substitute values into the formula

Substitute $x_1 = 1$, $y_1 = 4$ and $m=4$ into the point - slope form:
$y - 4=4(x - 1)$

Step3: Simplify the equation

Expand the right - hand side: $y-4 = 4x-4$
Add 4 to both sides of the equation: $y=4x-4 + 4$
Simplify the right - hand side: $y = 4x$

Answer:

The equation of the line is $y = 4x$ (or in standard form $4x-y=0$)