Slope of a Line

Slope of  aline is the inclination of the lien with the horizontal. The slope of  ahorizontal line is zeroa nd that of a vertical line is infinity. Slope of a line can be positive or negative depending on the direction of inclination. By definition, slope of a line is the tangent of the angle between the line and the positive x-axis measured counter clockwise.

The slope of the line is one of the factors in the equation of a line. When the equation of the line given by the slope intercept form that is y=mx+b. here m is the slope of the line and b is the constant term . from  this equation we can find the slope of the line and the x and y intercept of the line.
The equation is y=mx+b, m is the slope. This form of a line's equation is slope intercept form, because b acts as the y-intercept of the line, it is a point  where the line meets the y-axis.


Formula for slope (slope (m) and point are known) in algebra

If the slope of a line and a point (x1, y1) on the line are both known, then the equation of the line can be found using the point-slope formula:

y- y1= m (x-x1)

Example problems:

1.what is the slope-intercept form of the line that contains one point and a slope that is  (-1, 4) with a slope 1/4.

Solution:

y - y1 = m(x - x1)

It goes through the point (-1,3) and has a slope of 1/4.  So plug in  this values into the point-slope formula gives:

y - 4 = `1/4(x - (-1))`
y - 4 = `1/4(x + 1)`
y - 4 = `x/4 + 1/4`
y = `x/4 + 1/4 + 4`
y = `x/4 + 1/4 + 16/4`
y = `x/4+ 17/4 `
The final answer  is in slope-intercept form of the given line , which is y = mx + b, where m is the slope and b is the y-intercept or constant

model problems to slope formula in algebra

write the slope-intercept  of the line that passes through (7, 0) that is perpendicular to the line x + y = 4.

Solution:

If two lines are perpendicularto each other  then their slopes are negative reciprocal to each other.  So find the slope of the line given:
x + y = 4
y = -x + 4
.

So the slope is -1.  The minus reciprocal of -1 is 1.  So put that into the point-slope formula:

y - 0 = 1(x - 7)
y = x – 7.