Question

let’s start with the equation for the slope of a line, m, through any two points ((x_1, y_1)) and ((x_2, y_2)). (\frac{y_2 - y_1}{x_2 - x_1} = m) step 1: complete the substitution, using ((0, b)) for ((x_1, y_1)) and ((x, y)) for ((x_2, y_2)) in the above equation. (\frac{y - square}{square - square} = m) step 2: simplify the denominator (\frac{y - square}{square} = m) step 3: eliminate the fraction (y - square = m cdot square) step 4: solve for y (y = m cdot square + square)

Explanation:

Step1: Substitute the points

We have the slope formula $\frac{y_2 - y_1}{x_2 - x_1}=m$. Substituting $(x_1,y_1)=(0,b)$ and $(x_2,y_2)=(x,y)$, we get $\frac{y - b}{x - 0}=m$.

Step2: Simplify the denominator

Simplify $x - 0$ to $x$, so the equation becomes $\frac{y - b}{x}=m$.

Step3: Eliminate the fraction

Multiply both sides of the equation $\frac{y - b}{x}=m$ by $x$ to get $y - b=m\cdot x$.

Step4: Solve for y

Add $b$ to both sides of the equation $y - b=m\cdot x$ to get $y=m\cdot x + b$.

Answer:

Step 1: $\frac{y - \boldsymbol{b}}{x - \boldsymbol{0}} = m$
Step 2: $\frac{y - \boldsymbol{b}}{\boldsymbol{x}} = m$
Step 3: $y - \boldsymbol{b} = m\cdot\boldsymbol{x}$
Step 4: $y = m\cdot\boldsymbol{x} + \boldsymbol{b}$