Question

my hw write find an equation of the line passing through (-2,3) and (4,-5) I have to write the equation in slope-intercept form I need help

Answer 1

The line passing through the given points is:

`y=-(4)/(3)x+(1)/(3)`

in its slope-intercept form

Explanation:

Start by finding the slope of the segment that joins the two given points using the slope formula:

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

which for our case renders:

`slope=(3-(-5))/(-2-4)=(8)/(-6) =-(4)/(3)`

Now we can find the y-intercept by using any one of the given points in the general slope-intercept form of a line with this slope:

`y=-(4)/(3) x+b\\3=-(4)/(3) (-2)+b\\3=(8)/(3)+b\\b=3-(8)/(3) \\b=(9-8)/(3) \\b=(1)/(3)`

Therefore, the equation of the line becomes:

`y=-(4)/(3)x+(1)/(3)`