Question

Please help me.

What is the equation of the line?

Answer 1

`y = (-7)/(3)x -12`

Explanation:

Point-slope form is
`y-y_1= m (x-x_1)`. The
`m`,
`x_1`, and
`y_1` have to be substituted for with real values in order to make an equation of a line. From there, you can isolate
`y` to turn it into slope-intercept form.

1) First, let's find the slope of the line, which is represented by the variable
`m`. Use the slope formula,
`(y_2-y_1)/(x_2-x_1)`, to find the slope.
`x_1` and
`y_1` are the x and y values of one point,
`x_2` and
`y_2` are the x and y values of another point. For this problem, let's use the given points (-3, -5) and (-6, 2):

`((2)-(-5))/((-6)-(-3)) \\= (2+5)/(-6+3) \\= (7)/(-3)`

Thus, the slope is
`(7)/(-3)`.

2) Now that we have the slope, let's substitute it into the point-slope formula. The
`x_1` and
`y_1` represent the x and y values of a point that the line intersects so you could either use (-3, -5) or (-6,2), but for this answer, I used (-6,2). (The answer will always be the same no matter which point you choose.) Substitute these values then isolate y to put it in slope-intercept form:

`y-(2) = (-7)/(3) (x-(-6))\\y -2 = (-7)/(3) (x+6)\\y-2 = (-7)/(3)x-(42)/(3) \\y -2 = (-7)/(3)x-14\\y = (-7)/(3)x-12`

So,
`y = (-7)/(3)x -12` is the answer.