All Common Core: 8th Grade Math Resources
Example Questions
例子问题# 1:Use Similar Triangles To Show Equal Slopes: Ccss.Math.Content.8.Ee.B.6
A line has the equation. What is the slope of this line?
You need to put the equation inform before you can easily find out its slope.
Since, that must be the slope.
例子问题# 1:Slope
The equation of a line is. Find the slope of this line.
To find the slope, you will need to put the equation inform. The value ofwill be the slope.
Subtractfrom either side:
Divide each side by:
You can now easily identify the value of.
例子问题# 1:Use Similar Triangles To Show Equal Slopes: Ccss.Math.Content.8.Ee.B.6
What is the-intercept of the graph of the function?
The-intercept of the graph of a function is the point at which it intersects the-axis - that is, at which. This point is, so evaluate:
The-intercept is.
例子问题# 1:How To Find X Or Y Intercept
Give the-intercept, if there is one, of the graph of the equation
The graph has no-intercept.
The graph has no-intercept.
The-intercept is the point at which the graph crosses the-axis; at this point, the-coordinate is 0, so substituteforin the equation:
However, since this expression has 0 in a denominator, it is of undefined value. This means that there is no value ofpaired with-coordinate 0, and, subsequently, the graph of the equation has no-intercept.
例子问题# 1:How To Find X Or Y Intercept
Give the-intercept, if there is one, of the graph of the equation
The graph has no-intercept.
The-intercept is the point at which the graph crosses the-axis; at this point, the-coordinate is 0, so substituteforin the equation:
The-intercept is.
Example Question #4 :How To Find X Or Y Intercept
Give the-intercept, if there is one, of the graph of the equation
.
The graph does not have a-intercept.
The-intercept is the point at which the graph crosses the-axis; at this point, the-coordinate is 0, so substituteforin the equation:
The-intercept is the point.
Example Question #5 :How To Find X Or Y Intercept
A line passes throughand is perpendicular to the line of the equation. Give the-intercept of this line.
The line has no-intercept.
First, find the slope of the second lineby solving foras follows:
The equation is now in the slope-intercept form; the slope of the second line is the-coefficient.
The first line, being perpendicular to the second, has as its slope the opposite of the reciprocal of, which is.
Therefore, we are looking for a line throughwith slope. Using point-slope form
with
,
the equation becomes
.
To find the-intercept, substitute 0 forand solve for:
The-intercept is the point.
例子问题# 1:X And Y Intercept
A line passes throughand is parallel to the line of the equation. Give the-intercept of this line.
The line has no-intercept.
First, find the slope of the second lineby solving foras follows:
The equation is now in the slope-intercept form; the slope of the second line is the-coefficient.
The first line, being parallel to the second, has the same slope.
Therefore, we are looking for a line throughwith slope. Using point-slope form
with
,
the equation becomes
.
To find the-intercept, substitute 0 forand solve for:
The-intercept is the point.
Example Question #7 :How To Find X Or Y Intercept
Give the-intercept of the line with slopethat passes through point.
The line has no-intercept.
By the point-slope formula, this line has the equation
where
By substitution, the equation becomes
To find the-intercept, substitute 0 forand solve for:
The-intercept is the point.
Example Question #8 :How To Find X Or Y Intercept
Give the-intercept of the line that passes through pointsand.
The line has no-intercept.
First, find the slope of the line, using the slope formula
setting:
By the point-slope formula, this line has the equation
where
; the line becomes
or
To find the-intercept, substitute 0 forand solve for:
The-intercept is.