Question

Find an equation for the line with the given properties.
x-intercept = 2; y-intercept = -3. y =

Answer 1

Answer:

$y=\displaystyle\frac{3}{2}x-3$

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x=0)

We're given:

⇒ x-intercept = 2

⇒ y-intercept = -3

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 $(x_2,y_2)$

Given the x- and y-intercepts, we can rewrite them as points:

x-intercept = 2

⇒ (2,0)

y-intercept = -3

⇒ (0,-3)

Plug these points into the equation:

$m=\displaystyle\frac{0-(-3)}{2-0}\\\\m=\displaystyle\frac{0+3}{2}\\\\m=\displaystyle\frac{3}{2}$

Therefore, the slope of the line is $\displaystyle\frac{3}{2}$. Plug this into $y=mx+b$:

$y=\displaystyle\frac{3}{2}x+b$

2) Plug in the y-intercept (b)

$y=\displaystyle\frac{3}{2}x+b$

We're given the y-intercept: -3. Plug this into $y=\displaystyle\frac{3}{2}x+b$:

$y=\displaystyle\frac{3}{2}x+(-3)\\\\y=\displaystyle\frac{3}{2}x-3$

I hope this helps!