Question

write the equation of the line in slope - intercept form that passes through the points (4, 5) and (6, 8). (hint: you have two points so run a regression!) y=-x+\frac{3}{2} y = -\frac{3}{2}x + 2 y=\frac{2}{3}x + 8 y=\frac{3}{2}x - 1

Explanation:

Step1: Calculate the slope

The slope $m$ formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $(x_1,y_1)=(4,5)$ and $(x_2,y_2)=(6,8)$, then $m=\frac{8 - 5}{6 - 4}=\frac{3}{2}$.

Step2: Find the y - intercept

Use the slope - intercept form $y=mx + b$ and one of the points, say $(4,5)$. Substitute $x = 4$, $y = 5$ and $m=\frac{3}{2}$ into $y=mx + b$. We get $5=\frac{3}{2}\times4 + b$. Simplify the right - hand side: $\frac{3}{2}\times4=6$, so $5 = 6 + b$. Solve for $b$: $b=5 - 6=-1$.

Step3: Write the equation

The equation of the line in slope - intercept form is $y=\frac{3}{2}x-1$.

Answer:

$y=\frac{3}{2}x - 1$ (corresponding to the last option in the multiple - choice list)