Question

Write the equation of the line with x-intercept 3 and passing through the point (5, 4)

Answer 1

Answer: The required equation of the line is
`y=2x-6.`

Step-by-step explanation: We are give to write the equation of a straight line with x-intercept 3 and passing through the point (5, 4).

Since the given line has x-intercept 3, so it will pass through the point (3, 0).

The slope of a line passing through the points (a, b) and (c, d) is given by

`m=(d-b)/(c-a).`

Since the given line passes through the points (3, 0) and (5, 4), so its slope will be

`m=(4-0)/(5-3)=(4)/(2)=2.`

Therefore, the equation of the line is given by

`y-0=m(x-3)\\\\\Rightarrow y=2(x-3)\\\\\Rightarrow y=2x-6.`

Thus, the required equation of the line is
`y=2x-6.`

Answer 2

y=2x-6

Explanation:

The line has an x-intercept of (3,0) and crosses through the point (5,4). Using these points, we can find the slope using the slope formula.

`m=(y_2-y_1)/(x_2-x_1)= (4-0)/(5-3) =(4)/(2)=2`

To write the equation of the line, substitute m=2 and the point (5,4) into the
`y-y_1 = m(x-x_1)`.

`y-4=2(x-5)\\y-4=2x-10\\y=2x-6`