Question

The points −4, r and 3, 3 lie on a line with slope −4. Find the missing coordinate r. r=

Answer 1

r = 31

Step-by-step explanation:

If a point (x0, y0) lies on a line with slope m, then the equation of the line in slope-intercept form is given by

`y-y_0=m(x-x_0)`

Now in our case, we know that the point (3, 3) lies on the line and the slope is -4. Therefore, (x0, y0) = (3, 3) and m = -4 and the above formula gives

`y-3=-4(x-3)`

which is the equation of the line in slope-intercept form.

Now to find the value of r for the point (-4, r), we put in x = -4 to get

`r-3=-4(-4-3)`

which simplifies to give

`r-3=-4*(-7)`
`r-3=28`

finally, adding 3 to both sides gives

`\boxed{r=31.}`

which is our answer!