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Equation of a Line

Q: What is the equation of a line?

A: The equation of a line is y=mx+b, where

m = slope

b = y-intercept

Q: What is slope?

A: The slope of a line is a measure of how steep the line is. A larger slope means that the line is steeper, while a smaller . . . → Read More: Equation of a Line

Finding the y-intercept

Q: The equation of a line is y=2x -7. What is the y-intercept?

A: It is easy enough to simply compare the equation to the standard form, y=mx+b, and see that b = -7.

However, the general way to find the y-intercept is to set x=0, and solve for y.

y = 2(0) – . . . → Read More: Finding the y-intercept

Finding the Slope

Q: Can you show me how to find the slope of a line with the equation (y+3)=5(x-2)?

A: First, turn the equation into slope-intercept form, y=mx+b. Do this by isolating for y in the equation.

y + 3 = 5x – 10 y = 5x – 10 – 3 y = 5x – 13

. . . → Read More: Finding the Slope

Finding the slope between two points

Q: What is the slope of a line that contains the two points (0,3) and (4,5) ?

A: Recall that the equation for slope is:

You have two points, (0,3) and (4,5), so you have (x1,y1) and (x2,y2). Put them into the formula:

m = (5-3) / (4-0) m = 2 / 4 . . . → Read More: Finding the slope between two points

Slopes and Equations of Parallel Lines

Q: Please show me how to write an equation that is the slope-intercept form of the equation of the line that passes through (1,2) and is parallel to 4x-2y=6

A: This looks hard at first, but it’s actually not too bad.

First, let’s rearrange the 4x-2y=6 line so that it’s in slope-intercept form, y=mx+b

. . . → Read More: Slopes and Equations of Parallel Lines