Respuesta :

Omega314

Answer:

[tex]k=\frac{13}{2}[/tex]

Step-by-step explanation:

The equation [tex]y=2x+c[/tex] is a linear equation. By definition, the independent term on this equation (that is, the number that is not being multiplied by [tex]x[/tex]) is the y-intercept, which is a fancy way of saying "the point where the line crosses the y-axis".

By looking at the equation, we know that our y-intercept is c. By looking at the graph, we can see that the y-intercept is -3. Therefore, [tex]c=-3[/tex] and we get the complete version of our linear equation:

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

Now, looking at the graph we can see that the point [tex](k,10)[/tex] lies on the line of the equation, which means that the point is a solution to our equation. All we have to do is replace [tex]x[/tex] and [tex]y[/tex] by the values of the given point (which are [tex]k[/tex] and [tex]10[/tex], respectively), and then solve for [tex]k[/tex]:

[tex]10=2k-3\\10+3=2k\\13=2k\\2k=13\\k=\frac{13}{2}[/tex]

And we are done!

onyebuchinnaji

The value of k in the given coordinate points is 6.5

The given equation of line;

y = 2x + c

The slope of the line, m = 2

The value of c is calculated as follows;

From the graph, the y-intercept = -3

Thus, the value of c = -3

The complete form of the equation;

y = 2x - 3

The value of  k is calculated as follows;

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

in the given graph we can identify the following;

y₂ = 10,  and    y₁ = -3

x₂ = k    and     x₁ = 0

[tex]\frac{10 - (-3)}{k-0} = 2\\\\\frac{13}{k} = 2\\\\k = \frac{13}{2} \\\\k = 6.5[/tex]

Thus, the value of k in the given coordinate points is 6.5

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