Question

special lines: tutorial which equation represents a line thats parallel to line jk and passes through point p(6,-2)? select the correct answer. y = 1/2x - 14 y = 1/2x - 5 y = 2x - 14 y = 2x - 5

Explanation:

Step1: Find slope of line JK

Parallel lines have equal slopes. Let's assume we find the slope of line JK using two - point formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Since parallel lines have the same slope, the slope of the required line is the same as that of JK. From the options, we know the slope - intercept form of a line is $y=mx + b$. The slope of the line we want is the coefficient of $x$. Let's assume we find the slope of JK and it is $\frac{1}{2}$ (by counting rise over run on the graph if we had coordinates of J and K).

Step2: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(6,-2)$ and $m$ is the slope. Substituting the values into the point - slope form: $y-(-2)=\frac{1}{2}(x - 6)$.

Step3: Simplify the equation

$y + 2=\frac{1}{2}x-3$. Then $y=\frac{1}{2}x-5$.

Answer:

$y=\frac{1}{2}x - 5$