Write an equation of the line that passes through the point (1,9) and has the slope 5.

Solution:

Equation of line passes through the point (x\(_1\),y\(_1\)) and the slope 5 is

(y - y\(_1\)) =m(x - x\(_1\))

Given x1 =1 and y1 = 9 and slope = 5

∴ Equation of the given line is

( y- 9) = 5(x -1)

On simplifying

⇒y - 9 = 5x - 5

⇒ y = 5x - 5 +9

⇒ y = 5x + 4

From the above graph it is observed that the line passing through the point (1,9) makes an intercept with the y-axis at 4 .

Which is the equation of line in slope-intercept form.

The equation of a line in slope-intercept form is.

Y = mx + c

Where m is the slope of the line

C is the intercept made by the y- axis.

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Write an equation of the line that passes through the point (1,9) and has the slope 5.

Summary:

Equation of the line through (1,9) and has slope 5 is y = 5x + 4