Write the slope-intercept form of the line that passes through the points (6, 1) and (5, 4)

Remember that the general equation for slope-intercept form is y = mx + b, where m = the slope of the equation, b = the y intercept, and x and y are your variables (and the coordinate points on the graph). 
First start by finding m, the slope. To find slope, use the equation:
where  and  are the x and y values of one coordinate point , and  and  are the x and y values of another coordinate point . Since we are given two coordinate points, that means we can find the slope using the slope equation. 
Let's choose (6, 1) as your  point and (5, 4) as your  point, but you can switch those if you want! That makes  and . Plug these values into the slope equation:


Now you know the slope of your line that passes through the points is m=-3. Plug that into your slope-intercept equation:
y = -3x +b 

Finally you want to find b. To find b, just plug in one of your coordinate points and solve for b. I'll use (6,1), but you can use either one!


Put b into your slope intercept equation to find your final equation of your line:
y = -3x + 19

The equation of your line is y = -3x + 19

exponential functions fit the template

y = a*b^x

where 'a' and b are fixed values

the value of 'a' is the y intercept. in this case, it is 100 since (0,100) is on the curve. this is the part where the graph crosses the y axis. so a = 100.

the value of b takes a bit of work to find. we'll plug a = 100, x = 1 and y = 50 into the equation shown above. why x = 1 and y = 50 you might ask? well the point (1,50) appears to be on the graph as well.

so plugging those three items into the equation leads to

y = a*b^x

50 = 100*b^1

50 = 100*b

50/100 = 100*b/100 divide both sides by 100

1/2 = b

b = 1/2 

b = 0.5

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step-by-step explanation: