jtwum4
contestada

find the equations of the straight line which passes through the following points C(1,5) and D(3,9)​

Respuesta :

To find the equation of the straight line passing through points \(C(1,5)\) and \(D(3,9)\), we can use the point-slope form of the equation for a straight line:

\(y - y_1 = m(x - x_1)\)

where \(m\) is the slope of the line and \((x_1, y_1)\) is one of the given points.

First, let's find the slope (\(m\)) using the given points \(C\) and \(D\):

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Substituting the given points:

\(m = \frac{9 - 5}{3 - 1} = \frac{4}{2} = 2\)

Now that we have the slope, let's choose point \(C(1,5)\) to substitute into the point-slope form:

\(y - 5 = 2(x - 1)\)

Now, we can simplify this equation:

\(y - 5 = 2x - 2\)

Add 5 to both sides:

\(y = 2x + 3\)

So, the equation of the straight line passing through points C(1,5) and D(3,9)is (y = 2x + 3).
msm555

Answer:

[tex]\sf y = 2x + 3[/tex]

Step-by-step explanation:

To find the equation of the straight line passing through points [tex]\sf C(1,5)[/tex] and [tex]\sf D(3,9)[/tex], we can use the point-slope form of the equation of a line:

[tex]y - y_1 = m(x - x_1)[/tex]

where

  • [tex]\sf m[/tex] is the slope of the line, and
  • [tex]\sf (x_1, y_1)[/tex] is a point on the line.

First, let's find the slope ([tex]\sf m[/tex]) using the coordinates of points [tex]\sf C[/tex] and [tex]\sf D[/tex]:

[tex]m = \dfrac{{y_2 - y_1}}{{x_2 - x_1}}[/tex]

where [tex]\sf x_1 = 1[/tex], [tex]\sf y_1 = 5[/tex], [tex]\sf x_2 = 3[/tex], and [tex]\sf y_2 = 9[/tex].

[tex]m = \dfrac{{9 - 5}}{{3 - 1}} = \dfrac{4}{2} = 2[/tex]

Now that we have the slope, let's choose one of the points, say [tex]\sf C(1,5)[/tex], and substitute the coordinates and the slope into the point-slope form:

[tex]y - 5 = 2(x - 1)[/tex]

Now, we can simplify and rewrite the equation in slope-intercept form ([tex]\sf y = mx + b[/tex]):

[tex]y - 5 = 2x - 2[/tex]

[tex]y = 2x - 2 + 5[/tex]

[tex]y = 2x + 3[/tex]

So, the equation of the straight line passing through points [tex]\sf C(1,5)[/tex] and [tex]\sf D(3,9)[/tex] is:

[tex]\sf y = 2x + 3[/tex]

Otras preguntas