You need to determine another point along the line or determine the slope of the line given the graph.
First, count the "rise" and "run" units along the graphs. To count the "rise" units, count the number of units it takes for the line to rise up. To count the "run" units, count the number of units it takes for the line to run left/right.
Remember:
Use this simplified form:
m = slope form = rise / run
Then, use the point-slope form to determine the equation of a line.
y - y0 = m(x - x0)
To find the parametric equations of a line, you need a point on the line and a direction vector. If you have a point ( P(x_0, y_0, z_0) ) and a direction vector ( \mathbf{d} = \langle a, b, c \rangle ), the parametric equations can be expressed as: ( x = x_0 + at ), ( y = y_0 + bt ), and ( z = z_0 + ct ), where ( t ) is a parameter. This representation allows you to express every point on the line as ( t ) varies.
y-4=3/2(x-7)
To find the solution of two equations graphed on a coordinate plane, look for the point where the two lines intersect. This point represents the values of the variables that satisfy both equations simultaneously. The coordinates of this intersection point are the solution to the system of equations. If the lines are parallel, there is no solution; if they are the same line, there are infinitely many solutions.
True. In Euclidean geometry, if there is a line and a point not on that line, there exists exactly one line that can be drawn through the point that is parallel to the given line. This is known as the Parallel Postulate, which states that for a given line and a point not on it, there is one and only one line parallel to the given line that passes through the point.
You need either a point and the slope of the line or two points. Then you use the point slope form of the line or the slope intercept form to write the lines.A given point has an infinite number of lines going through it, that is why you need more information.
Parallel straight line equations have the same slope but with different y intercepts
To find the parametric equations of a line, you need a point on the line and a direction vector. If you have a point ( P(x_0, y_0, z_0) ) and a direction vector ( \mathbf{d} = \langle a, b, c \rangle ), the parametric equations can be expressed as: ( x = x_0 + at ), ( y = y_0 + bt ), and ( z = z_0 + ct ), where ( t ) is a parameter. This representation allows you to express every point on the line as ( t ) varies.
Both straight line equations will have the same slope or gradient but the y intercepts wll be different
y-4=3/2(x-7)
Points: (4, -2) Equation: 2x -y -5 = 0 Perpendicular equation: x+2y = 0 Both equations intersect at: (2 -1) Prependicular distance is the square root of (4-2)2+(-2--1)2 So the distance is the square root of 5 Knowing the equation of the line, you can work out the gradient of a line perpendicular to the line: Given the line in the form y = mx + c (where m is the gradient of the line and c is the y-intercept), the gradient of a perpendicular line (m') is given by: mm' = -1 → m' = -1/m The equation of the line perpendicular to the given line through a given point (xo, yo) can then be found by: y - yo = m'(x - xo) = -1/m(x - xo) With the two lines you can find their point of intersection, namely the point (xi, yi) that simultaneously satisfies both equations, and then use Pythagoras to find the distance from this point to the given point: distance = √((xo - xi)2 + (yo - yi)2)
To find the solution of two equations graphed on a coordinate plane, look for the point where the two lines intersect. This point represents the values of the variables that satisfy both equations simultaneously. The coordinates of this intersection point are the solution to the system of equations. If the lines are parallel, there is no solution; if they are the same line, there are infinitely many solutions.
is it a line that is slanted
True. In Euclidean geometry, if there is a line and a point not on that line, there exists exactly one line that can be drawn through the point that is parallel to the given line. This is known as the Parallel Postulate, which states that for a given line and a point not on it, there is one and only one line parallel to the given line that passes through the point.
Two points determine a line. Also there is one and only line perpendicular to given line through a given point on the line,. and There is one and only line parallel to given line through a given point not on the line.
You need either a point and the slope of the line or two points. Then you use the point slope form of the line or the slope intercept form to write the lines.A given point has an infinite number of lines going through it, that is why you need more information.
From a given line at a specific point, there can be exactly one circle tangent to the line at that point. This circle will have its center located on the perpendicular line drawn from the point to the line. The radius of the circle will be the distance from the center to the point of tangency.
To measure the point at which two tangents intersect each other, find an equation for each tangent line and compute the intersection. The tangent is the slope of a curve at a point. Knowing that slope and the coordinates of that point, you can determine the equation of the tangent line using one of the forms of a line such as point-slope, point-point, point-intercept, etc. Do the same for the other tangent. Solve the two equations as a system of two equations in two unknowns and you will have the point of intersection.