Question

Write the equation in slope intercept form: passing through the x-axis at x=3 and passing through the y-axis at y= -5

Answer 1

`y=(5)/(3)x-5`

Explanation:

Slope-intercept:

`y=mx+b`

m is the slope and b is the y-intercept. We know that the line passes through the y-axis at -5, so this is the y-intercept (where x is equal to 0). Insert this into the equation:

`y=mx-5`

With the given information, we can form two points:

`(3,0)(0,-5)`

The first one is the x-intercept and the second the y-intercept. Use these to find the slope:

`(y_(2)-y_(1))/(x_(2)-x_(1))=(rise)/(run)`

Rise over run is the change in the y-axis over the change in the x-axis, otherwise known as the slope. Insert the appropriate values:

`(3_(x1),0_(y1))\\(0_(x2),-5_(y2))\\\\(-5-0)/(0-3)`

Solve:

`(-5-0)/(0-3)=(-5)/(-3)`

Note that both the numerator and denominator are negatives. Two negatives make a positive, so:

`(5)/(3)`

The slope is
`(5)/(3)`

Insert into the equation:

`y=(5)/(3)x-5`

:Done