Question

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

Answer 1

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:$m = slope = \frac{ y_{2} - y_{1} }{x_{2}-x_{1}}$
where $x_{2}$ and $y_{2}$ are the x and y values of one coordinate point , and $x_{1}$ and $y_{1}$ 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 $(x_{2}, y_{2})$ point and (5, 4) as your $(x_{1}, y_{1})$ point, but you can switch those if you want! That makes $x_{2} = 6, y_{2} = 1$ and $x_{1} = 5, y_{1} = 4$. Plug these values into the slope equation:
$slope = \frac{ y_{2} - y_{1} }{x_{2}-x_{1}}\\ slope = \frac{1-4}{6-5} \\ slope = -3$

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!
$y = -3x +b\\ 1 = -3(6) + b\\ 1 = -18 + b\\ b = 19$

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