Slope-intercept form is: y=mx+b, where m=slope and b=y-intercept (or starting point). Because this is a function (an equation in which relies on an x value to determine a y value), x=input and y=output. You can think of x as an independent variable since it is simply an input number, and y as a dependent variable because it depends on the value of x to determine a y value.
Furthermore, in y=mx+b, m=slope. Remember that slope is the change in y values over the change in x values, or more commonly known as rise over run. Essentially, the slope is the rate at which x is increasing, hence why m and x are multiplying each other as mx. The constant “b,” is the y-intercept; it is the point where the graph crosses the y-axis. It os also known as the starting point, where x=0 and y is the initial value in which the slope increases. This is why y=mx+b is called slope-intercept form; it has a slope and y-intercept.
Knowing this, let’s transform the information into a slope-intercept equation.
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1.) slope=9/4, y-intercept=-4
Remember that slope=m and y-intercept=b, so we can replace “slope” and “y-intercept” with these variables.
m=9/4 and b=-4
Now, substitute these values into the equation y=mx+b.
y=(9/4)x-4
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2.) m=-7/4, b=5
y=(-7/4)x+5
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3.) m=2, b=4
y=2x+4
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4.) m=-1/2, b=-2
y=(-1/2)x-2