Question

Write an equation of the line in slope-intercept form. JY 1 (3, 3) (0, 2) 2 4y=​

Answer 1

Correct answer: y = $\frac{1}{3}$x + 2

To find out the slope, you would need to remember this slope formula: $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$. We can use the two points provided on the graph to figure out the slope. We can label (3, 3) as $x_{1}$ and $y_{1}$, and (0, 2) as $x_{2}$ and $y_{2}$. Now we can plug these numbers into the slope formula to find out the slope:

m = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ → $\frac{2-3}{0-3}$ → $\frac{-1}{-3}$ → $\frac{1}{3}$

To find out the y-intercept, just substitute (3, 3) into the slope-intercept formula ( y = mx + b ) with the slope that is substituted for 'm' that we already solved earlier.

y = mx + b

(3) = $\frac{1}{3}$(3) + b

3 = 1 + b

2 = b

You can also prove this true by looking at the graph provided. The line intersects at the y-axis at 2.

Now we know that m = $\frac{1}{3}$ and b = 2, we can substitute it into the slope-intercept formula. Thus, the answer is y = $\frac{1}{3}$x + 2.

Hope this helps you! Let me know if you have any more questions related to this problem.