Question

WRITE AN EQUATION THAT REPRESENTS THE LINE. USE EXACT NUMBERS.

Answer 1

Answer:

$y=\frac{6}{5}x-5$

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 x is 0)

1) Determine the slope (m)

$m=\frac{y_2-y_1}{x_2-x_1}$

Plug in the two given points (0,-5) and (5,1)

$m=\frac{1-(-5)}{5-0}\\m=\frac{1+5}{5-0}\\m=\frac{6}{5}$

Therefore, the slope of the line is $\frac{6}{5}$. Plug this into $y=mx+b$:

$y=\frac{6}{5}x+b$

2) Determine the y-intercept (b)

$y=\frac{6}{5}x+b$

On the graph, we can see that when x is 0, y is equal to -5 (we're also given the point (0,-5). Therefore, the y-intercept of the line is -5. Plug this back into the equation:

$y=\frac{6}{5}x-5$

I hope this helps!

Answer 2

Answer:

y = 6/5x - 5

Step-by-step explanation:

To find the equation of a linear line you need 2 things: the slope and the y-intercept.

The slope can be found by taking two points and dividing the change in y by the change in x. Using the two points highlighted, the slope would be (1 - -5)/(5-0) = 6/5.

The y-intercept is where the line crosses the y-axis, which on this line is at -5. Then plug in this information into point slope form, y = mx + b, where m is the slope.

So you get y = 6/5x - 5.

Here is standard form too if you need this instead: 6x - 5y = 25