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# How to Find a Slope of a Line

Updated: Apr 28

What is a slope? The slope represents the change in the y coordinates over the change in the x coordinates between two points on a line. In other words, slope = change in y / change in x Standard form of a linear equation. Ax + By = C Slope intercept form of a linear equation Y= mx + b (m represents the slope; b represents the y-intercept)

HOW TO FIND THE SLOPE GIVEN AN EQUATION 1) Change equation to slope intercept form by isolating Y 2) Observe equation for “ m” which is the slope Example 1: Y = 3 X + 5 ======= > Already in slope intercept form Y = mx + b Slope = 3 or 3/1 or m = 3 or m = 3/1; normally it is written as m = 3 Example 2: 8x + 4y = 12 8x – 8x + 4y = 12 – 8x ===== > Subtract 8x from both sides 4y = 12 – 8x 4y/4 = 12/4 – 8x/4 ======= > Divide both sides by 4 Y = 3 – 2x Y = -2x + 3 ============== > Slope Intercept Form Y= mx +b Thus slope = -2 or m = -2

FINDING THE SLOPE GIVEN TWO POINTS: (X1, Y1) and (X2, Y2) As usual, there is a formula for this task ==== > m = Y2 – Y1 / X2 – X1 Remember, slope represents the change in the y- coordinates which is the numerator over the change in the x- coordinates which is the denominator. The word “change” tells us to find the difference or to subtract the first coordinate from the second coordinate. Example 3: (3, 1) and (5, 4) Let’s identify the coordinates. X1 = 3 Y1 = 1 X2 = 5 Y2 = 4 Next, plug into the formula M = 4 - 1 / 5 - 3 M = 3 / 2 Note: Something, you may not have considered. Take a moment and look at the slope formula again. m = Y2 – Y1 / X2 – X1 Notice Y2 is first in the numerator and X2 is first in the denominator. However, it’s okay to subtract the second coordinate from the first coordinate, but you must be consistent and do it for the numerator and denominator. Let’s try it. M = Y1 – Y2 / X1 – X2 M = 1 – 4 / 3 - 5 M = -3 / -2 M = 3/2

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