Question

lesson 5 write an equation given the slope a...
what is the slope, y-intercept, and equation of this line?

Explanation:

Step1: Identify two points

Choose points on the line, e.g., $(0, 4)$ and $(2, 1)$.

Step2: Calculate the slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$

$$\begin{align*} m&=\frac{1-4}{2-0}\\ &=\frac{-3}{2} \end{align*}$$

Step3: Find y-intercept

The line crosses the y-axis at $(0, 4)$, so $b=4$.

Step4: Write line equation

Use slope-intercept form $y=mx+b$
$y=-\frac{3}{2}x+4$

Answer:

• Slope: $\boldsymbol{-\frac{3}{2}}$
• y-intercept: $\boldsymbol{4}$
• Equation: $\boldsymbol{y=-\frac{3}{2}x+4}$