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What is the equation of a line with a slope of 7 and a point (1, 8) on the line?

Express the equation in the form of y = mx + b, where m is the slope and b is the y-intercept.


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ANSWER

The required equation is

[tex]y = 7 x+ 1[/tex]

EXPLANATION

Let the equation of the line be

[tex]y = mx + b...(1)[/tex]
where
[tex]m = 7[/tex]
is the slope of the line. We substitute this value of the slope into the equation (1) to obtain,


[tex]y = 7x + b...(2)[/tex]


Since the point (1,8) lies on the line, it must satisfy this equation.



We substitute the x and y value of the point into the equation(2) to get,

[tex] 8 = 7(1) + b[/tex]

This simplifies to give us,

[tex]8=7+b [/tex]


We solve for b to get,

[tex]b = 8 - 7[/tex]

[tex]b = 1[/tex]


We substitute the value of b back into equation (2) to get


[tex]y = 7x + 1[/tex]


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