The equation of the line which passes through (2,4) with a slope of 1/2 is [tex]y = \frac{x}{2} +3[/tex].
What is a slope-intercept form?
Y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept. X and y represent the distance of the line from x-axis and y-axis, respectively. The value of b is equal to y when x = 0, and m shows how steep the line is.
Given
Slope m = 1/2
Point (x, y) = (2, 4)
Equation of line which passes through a point (x, y) with a slope of m is
y = mx + b
Substitute the values
⇒ [tex]4=\frac{1}{2}(2)+b[/tex]
⇒ 4 = 1 + b
⇒ b = 4 - 1
⇒ b = 3
Substitute m = 1/2 and b = 3 in equation (1)
[tex]y = \frac{1}{2}(x) +3[/tex]
⇒ [tex]y = \frac{x}{2} +3[/tex]
Hence, the equation of the line which passes through (2,4) with a slope of 1/2 is [tex]y = \frac{x}{2} +3[/tex].
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