Question

How do you write the equation of a line given x intercept of 4 and a slope of \[\dfrac{3}{4}\] ?

Answer 1

Hint: We are given with the x intercept of 4 and a slope of \[\dfrac{3}{4}\] . This is an equation of a line in slope intercept form. We will just put the values of the intercepts and slope in the standard equation to get the equation of the line. X intercept is obtained when y is equals to zero.

Complete step-by-step solution:
Given that the x intercept of 4 and a slope of \[\dfrac{3}{4}\] a line is given.
We know that x intercept is nothing but a coordinate \[\left( {4,0} \right)\] satisfies the equation with slope \[\dfrac{3}{4}\].
Now comparing with general standard equation \[y = mx + c\]
Putting the values in the equation,
\[0 = \dfrac{3}{4} \times 4 + c\]
Cancelling 4 we get,
\[0 = 3 + c\]
Taking 3 on other side we get,
\[c = - 3\]
Now putting the values in standard equation we get,
\[y = \dfrac{3}{4}x - 3\]
This is the equation of the line so obtained.

Note: Slope is the ratio of vertical change to horizontal change. If the line is increasing then slope is positive and if line is decreasing then slope is negative. Also note that in geometrical cases the slope is given with the help of tan function.