Question

What is an equation of the line that passes through the points (-3,-1) and (6,2)?​

Answer 1

Answer:

$y=\frac{1}{3}x$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Determine the slope (m)

$m=\frac{y_2-y_1}{x_2-x_1}$ where two points the line passes through are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (-3,-1) and (6,2)

$=\frac{2-(-1)}{6-(-3)}\\=\frac{2+1}{6+3}\\=\frac{3}{9}\\=\frac{1}{3}$

Therefore, the slope of the line is $\frac{1}{3}$. Plug this into $y=mx+b$:

$y=\frac{1}{3}x+b$

2) Determine the y-intercept (b)

$y=\frac{1}{3}x+b$

Plug in one of the given points and solve for b

$2=\frac{1}{3}(6)+b\\2=2+b$

Subtract 2 from both sides to isolate b

$2-2=2+b-2\\0=b$

Therefore, the y-intercept is equal to 0. Plug this back into $y=\frac{1}{3}x+b$:

$y=\frac{1}{3}x+0\\y=\frac{1}{3}x$

I hope this helps!