Question

Find the equation of the line.
y=__x+__​

Answer 1

y = 4x - 9 is the equation of the line.

Answer 2

y=4x-9

Explanation:

The equation of a line is typically written in slope-intercept form, which is y=mx+b. Here's what the variables mean:

y=the y-coordinate

m=the slope

x=the x-coordinate

b=the y-intercept (the point on the line that intercepts the y-axis)

The only values that we have to calculate to find the equation are the slope of the line and the y-intercept. Let's start off by finding the slope.

To find the slope of a line, we would need to find 2 points that fall on the line,
`(x_1, y_1)` and
`(x_2, y_2)` and plug them into the expression
`(y_2-y_1)/(x_2-x_1)`. Let's use the points (1, -5) and (3, 3).

`(y_2-y_1)/(x_2-x_1)`

`(3-(-5))/(3-1)`

`=(3+5)/(3-1)\\= (8)/(2)\\= 4`

Therefore, the slope of the line is 4.

To find the y-intercept, all we need to do is look at which point the line crosses the y-axis, and that point is -9.

Finally, we plug the slope and the y-axis into the equation y=mx+b as m and b.

y=mx+b

y=4x-9

I hope this helps!