After knowing the basic method for graphing straight lines like plotting some points or draw a line, it is necessary to find the respective equations. 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.
What is the slope?
We usually think of the slope when we go to any mountainous area. We call it hitting the slope when a snowboarder 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.
Solved Examples
Example 1: Write the equation of the line in slope-intercept form with a slope of −3 and a y-intercept of 5.
Solution:
Given,
Slope = m = −3
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).
Solution:
Given,
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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