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:[tex]m = slope = \frac{ y_{2} - y_{1} }{x_{2}-x_{1}} [/tex]
where [tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the x and y values of one coordinate point , and [tex]x_{1}[/tex] and [tex]y_{1}[/tex] 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 [tex](x_{2}, y_{2})[/tex] point and (5, 4) as your [tex](x_{1}, y_{1})[/tex] point, but you can switch those if you want! That makes [tex]x_{2} = 6, y_{2} = 1[/tex] and [tex]x_{1} = 5, y_{1} = 4[/tex]. Plug these values into the slope equation:
[tex]slope = \frac{ y_{2} - y_{1} }{x_{2}-x_{1}}\\
slope = \frac{1-4}{6-5} \\
slope = -3 [/tex]
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!
[tex]y = -3x +b\\
1 = -3(6) + b\\
1 = -18 + b\\
b = 19[/tex]
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
