Question

the slope formula is used to find the steepness of a line. which of the following represents this formula?
a. \\(\frac{y_2 - y_1}{x_2 - x_1}\\)
b. \\(\frac{x_2 - x_1}{y_2 - y_1}\\)
c. \\(y_2 + y_1\\)
d. \\(x_2 + x_1\\)
a line with an undefined slope is:
a. slanted
b. diagonal
c. vertical
d. horizontal

Explanation:

First Question:

The slope formula for a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is defined as the change in \(y\) - values divided by the change in \(x\) - values. Mathematically, this is \(\frac{y_2 - y_1}{x_2 - x_1}\). Option a represents this formula. Option b has the change in \(x\) over the change in \(y\), which is not the slope formula. Options c and d are just sums of \(y\) - values and \(x\) - values respectively, and have nothing to do with the slope formula.

The slope of a line is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For a vertical line, the \(x\) - coordinates of all points on the line are the same, so \(x_2 - x_1 = 0\). Division by zero is undefined, so the slope of a vertical line is undefined. A slanted or diagonal line has a non - zero, defined slope. A horizontal line has a slope of 0 (since \(y_2 - y_1=0\) and \(x_2 - x_1
eq0\), so \(m = 0\)).

Answer:

a. \(\frac{y_2 - y_1}{x_2 - x_1}\)

Second Question: