Question

Write an equation of the line that passes through (2, -1) and (-3, 3). help please

Answer 1

Answer:

$y=-\displaystyle\frac{4}{5}x+\displaystyle\frac{3}{5}$

Step-by-step explanation:

Hi there!

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

1) Determine the slope (m)

$m=\displaystyle\frac{y_2-y_1}{x_2-x_1}$ where two points that fall on the line are $(x_1,y_1)$ and $(x_2,y_2)$

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

$m=\displaystyle\frac{-1-3}{2-(-3)}\\\\m=\displaystyle\frac{-4}{2+3}\\\\m=-\displaystyle\frac{4}{5}$

Therefore, the slope of the line is $-\displaystyle\frac{4}{5}$. Plug this into $y=mx+b$:

$y=-\displaystyle\frac{4}{5}x+b$

2) Determine the y-intercept (b)

$y=-\displaystyle\frac{4}{5}x+b$

Plug in one of the given points and solve for b:

$-1=-\displaystyle\frac{4}{5}(2)+b\\\\-1=-\displaystyle\frac{8}{5}+b\\\\b=\displaystyle\frac{3}{5}$

Therefore, the y-intercept is $\displaystyle\frac{3}{5}$. Plug this back into $y=-\displaystyle\frac{4}{5}x+b$:

$y=-\displaystyle\frac{4}{5}x+\displaystyle\frac{3}{5}$

I hope this helps!

Answer 2

Answer:

y= -0.8x + 0.6

Step-by-step explanation: