Question

What is the slope, y-intercept and equation for the line that passes through these points: (-1, -8), (-6, -33), (-10, -53) and (-13, -68)?

Answer 1

Equation of the line in slope-intercept form is `y =5 x -3` and y intercept is `y=-3`

Explanation:

The slope of the line passing through

`(-1,-8) and (-6,-33)` is

`m= (y_2-y_1)/(x_2-x_1)= (-33+8)/(-6+1)=(-25)/-5=5`

Let the equation of the line in slope-intercept form be

`y=m x+c or y=5 x+c` , the point (-1,-8) will satisfy

the equation . `:. -8= 5*(-1)+c or c= -8+5= -3`

Therefore , y intercept is `y=-3`

Hence the equation of the line in slope-intercept form is

`y= 5 x-3` . Check for points `(-10,-53) and (-13,-68)`

on the line , `y= 5 x -3 :. -53= 5 *(-10)-3` or

`-53 = -53 and -68= 5 *(-13)-3 or -68=-68`

Therefore all for points satisfy the equation of line.

Equation of the line in slope-intercept form is `y =5 x -3` and

y intercept is `y=-3`

graph{5 x-3 [-10, 10, -5, 5]} [Ans]