Question

FIFTY POINTS! PLS HELP QUICK!! the equation of a line that passes through (4,-5) and (0,-3).

Answer 1

Hello there! Your answer would be y = 0.5x - 3.

To find the equation, use slope intercept form, y = mx + b. (m = slope, b = y intercept)

For the slope, solve by subtracting the y values over the x values.

- 5 - - 3 / 0 - 4

- 2 / - 4

The negatives cancel out, and you are left with 0.5 as your slope. Plug that into m.

y = 0.5x + b

Now to find the y intercept. To do this, we can replace the x and y values into the equation and solve for b.

-5 = 0.5(4) + b

-5 = 2 + b

- 3 = b

so, the y intercept has a value of -3. Plug that in to the final equation.

y = 0.5x - 3

Hope this helps and have a great day!

Answer 2

Answer:

$y=-\frac{1}{2}x-3$

Step-by-step explanation:

When 2 points are given, we can use the point slope formula for a line to get the equation.

Point-Slope Form of a line:   $y-y_{1}=m(x-x_{1})$

Where,

• $(x_{1},y_{1})$ is point 1 and $(x_{2},y_{2})$ is point 2
• m is the slope and given by   $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Using the 2 points given and the formulas shown, we can write:

$y-(-5)=m(x-4)\\y+5=\frac{-3-(-5)}{0-4}(x-4)\\y+5=-\frac{2}{4}(x-4)\\y+5=-\frac{1}{2}(x-4)\\y+5=-\frac{1}{2}x+2\\y=-\frac{1}{2}x+2-5\\y=-\frac{1}{2}x-3$

Hence, $y=-\frac{1}{2}x-3$ is the equation of the line.