Respuesta :
Linear Equations
Linear equations are typically organized in slope-intercept form:
[tex]y=mx+b[/tex]
- m is the slope of the line
- b is the y-intercept (the value of y when the line passes through the y-axis)
To find linear equations in slope-intercept form:
- Determine the slope
- Plug the slope into the general form
- Determine the y-intercept by isolating b
- Plug the b back into the equation
Solving the Question
We're given:
- The line passes through the points (2,6) and (4,16)
First, determine the slope of the line.
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points that fall on the line
⇒ Plug in the given points (2,6) and (4,16):
[tex]m=\dfrac{16-6}{4-2}\\\\m=\dfrac{10}{2}\\\\m=5[/tex]
⇒ Therefore, the slope of the line is 5. Plug this back into the general form:
[tex]y=5x+b[/tex]
Now, determine the y-intercept.
[tex]y=5x+b[/tex]
⇒ Plug in one of the given points:
[tex]6=5(2)+b\\6=10+b\\b=-4[/tex]
⇒ Therefore, the y-intercept is -4. Plug this back into our original equation:
[tex]y=5x-4[/tex]
Answer
[tex]y=5x-4[/tex]