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4. Writing Linear Equations with Slope and a Point!
When given the slope (m) and a single point (x1, y1) , use the Slope-Intercept Form to write the equation: y = mx + b
Write the slope-intercept form: y = mx + b
Plug the value for slope under m. Plug the x and y values where they go too.
Solve for b.
Example: A line has a slope of 3 and goes through point (4, 19). What is the equation of this line?
Y = mx + b
19 = 3(4) + b
19 = 12 + b
b = 7
Therefore the equation of this line is: y = 4x + 7.
Another option: You may rewrite y = mx + b into the form b = y - mx. Observe:
b = y - mx
b = 19 - 3(4)
b = 19 - 12
b = 7
Just as before, the equation of this line is: y = 4x + 7.
Yet, another option: When given the slope (m) and a single point (x1, y1) , you might choose to use the Point-Slope Form to write the equation.
Point-Slope Form: y - y1 = m(x - x1)
Steps to Write the Equation
1. Plug in the slope(m) and the coordinates of the given point (x1, y1) into the point-slope formula:
• Example: Given m = 2 and point (3, 4) :
y - y1 = m(x - x1)
y - 4 = 2(x - 3) Distribute the right side of the equation…
y - 4 = 2x - 6 Add 4 to both sides of the equation…
Y = 2x - 6 + 4 Simplify…
Y = 2x - 2
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