Question 1203694
the slope intercept formula for a straight line is y = mx + b.
m is the slope.
b is the y intercept.


the formula for the slope is given as (y2 - y1) / (x2 - x1)


any two points on the line can be used.


the x-intercept is the value of x when y = 0.
you are given that the x-intercept is -2.
that means the point is (-2,0).


the y-intercept is the value of y when x = 0.
you are given that the y-intercept is -6.
that means the point is (0,-6).


your two poinjts are (-2,0) and (0,-6).
assign one of them to (x1,y1) and the other to (x2,y2).
either of the points can be assigned to either one of the constructs.
it doesn't matter.
the slope will be the same.


i'll assign two ways to show you what i mean.


first, i assigned (-2,0) to (x1,y1) and (0,-6) to (x2,y2)
slope = (y2-y1)/(x2-x1) = -6/2 = -3
next, i assigned (0,-6) to (x1,y1) and (-2,0) to (x2,y2)
slope = (y2-y1)/(x2-x1) = 6/-1 = -3
slope is -3 either way.


the slope is -3.
y = mx + b becomes y = -3x + b


to find the y-intercept, you need to replac4e x and y with any one of the points on the line and solve for b.
again, i'll do it using each point in turn.


first i used the point (0,-6).
y = -3x + b becomes -6 = -3 * 0 + b which becomes -6 = b.
solve for b to get b = -6.


next i used the point (-2,0).
y = -3x + b becomes 0 = -3 * -2 + b which becomes 0 = 6 * b.
solve for b to get b = -6.
y-intercept is -6 either way.


the equation becomes y = -3 * x - 6
the equation can be graphed as shown below.


<img src = "http://theo.x10hosting.com/2023/091701.jpg">