Question

For the equation \(y = mx + b\), what is the slope and y-intercept?

Answer 1

y-intercept: It is a point where the graph of a line touches or crosses the y-axis. The x-coordinate is zero at this point.
Finding the y-intercept: Put \(x = 0\) in \(y = mx + b\)
\(y = mx + b\)
\(\Rightarrow y = m(0) + b\)
\(\Rightarrow y = b\)
So, the y-intercept will be \((0, b)\) or \(y = b.\)
Since the graph of the line crosses the y-axis at \((0, b),\) let’s take two points \((x, y)\) and \((0, b)\) on the graph.
Slope \(= \dfrac{\text{Rise}}{\text{Run}}\)
\(= \dfrac{\text{Change in y}}{\text{Change in x}}\)
\(= \dfrac{y - b}{x - 0}\)
Slope \(= \dfrac{y - b} {x}\)
\(\Rightarrow y =\) (Slope) \(x + b\)
Comparing this with \(y = mx + b,\) we get:
\(m =\) Slope
\(\rightarrow\) Option D is correct.