After knowing the basic method for graphing straight lines like plotting some points or draw a line. The straight line equation is also called a slope-intercept form and it makes graphing easier.
If there are two points (a1, b1) and (a2, b2), The slope intercept formula for the straight line going through these given points will be
|y = mx + b
Where m = (b2 – b1)/(a2 – a1) and b = y-intercept
There are two important things that can help you graph an equation, slope and y-intercept.
We usually think of the slope when we go to any mountainous area. We call it hitting the slope when a snowboarders skews. On the graph, the steepness of a line is called the slope. It is the ratio of the change of y-value to the x-value. Using any two given points, you can find the slope using the above formula.
Example 1: Write the equation of the line in slope-intercept form with a slope of −3 and a y-intercept of 5.
Slope = m=−3 (slope)
y-intercept = b = 5
Substituting m and b values in y = mx + b,
y = mx + b
y = (-3)x + 5)
y = -5x + 3
This is the required line equation in slope intercept form.
Example 2: Write the equation of the line in slope-intercept with a slope of 7 and passing through the point (0, -4).
Slope = m = 7
Point = (x, y) = (0, -4)
We know that the equation of a line in slope intercept form is y = mx + b
Substituting the given values of m, x and y,
-4 = 7(0) + b
-4 = 0 + b
Therefore, b = -4 = y-intercept
Hence, the equation of line is:
y = mx + b
y = 7x – 4
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