Question

Find the equation of the line L in the form of y=mx +c

Answer 1

`y=4x+2`

Explanation:

According to the given graph we use x-intercept (-0.5, 0) and y-intercept (0, 2) to find the equation of the line using the two-point formula.

The two-point formula for finding the equation of a line passing through two points
`(x_1, y_1) and (x_2, y_2)`

Given points:

X-intercept: (-0.5, 0)(−0.5,0)

Y-intercept: (0, 2)(0,2)

Using the two-point formula:
`\\(y-y_1) = \frac{{y_2 - y_1}}{{x_2 - x_1}}*(x-x_1)`

`\\(y-0) = \frac{{2 - 0}}{{0 - (-0.5)}}*(x-(-0.5))`

`\\y = (2)/(0.5)*(x+0.5)\\\\y = 4*(x+0.5)\\y=4x+2`

As we can see, both the X-intercept and Y-intercept calculations result in the equation y = 4x + 2

So, the equation of the line passing through the x-intercept (-0.5, 0) and y-intercept (0, 2) is y = 4x + 2