Slope-intercept form: y = mx + b
[m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis]
Since you know:
m = -2 Substitute/plug it into the equation
y = mx + b
y = -2x + b To find b, plug in the point (7, -4) into the equation
-4 = -2(7) + b
-4 = -14 + b Add 14 on both sides to get "b" by itself
-4 + 14 = -14 + 14 + b
10 = b Now that you found b or the y-intercept, plug it in
y = -2x + 10
So to find the y-intercept, just plug in the point you were given into the equation once you had substituted in the slope. The slope tells you how many/the number of units from each point.
Slope can also be seen as:
"rise" is the number of units you go up(+ number) or down(- number) from each point. (y-axis)
"run" is the number of units you go to the right from each point (x-axis)
For example, if you were to graph this line,
you could first plot a point at the y-intercept (0, 10). To plot the next point, you use the slope -2 or -2/1. So from (0, 10) you would go down 2 units and to the right 1 unit, therefore the next point you would plot would be (1, 8)