Question

Determine the intercepts of the line.

Answer 1

x-intercept= (25,0)

y-intercept = (0,-55)

Explanation:

Directly:

We can easily find the x and y intercept for the straight line directly by looking from graph:

Look for the point where the line crosses the x-axis. This is the x-intercept. (25,0).

Look for the point where the line crosses the y-axis. This is the y-intercept.(0,-55).

`\hrulefill`

Indirectly:

let's take two points from (25,0) and (0,-55)

let's find the equation of the given line first.

The equation of a line passing through two points can be found using the point-slope form of linear equations, which is:

`\boxed{\tt y - y_1 = m(x - x_1)}`

where (x1, y1) is a point on the line and m is the slope of the line.

In this case, (x1, y1) = (25,0) and (x2, y2) = (0,-55).

The slope of the line can be calculated as follows:

`\tt m = ((y_2 - y_1) )/((x_2 - x_1) )=( (-55 - 0) )/((0 - 25)) = 2.2`

Substituting these values into the point-slope form of the equation, we get:

`\tt y - 0 = 2.2(x - 25)`

`y = 2.2x - 55`

Therefore, the equation of the line is y = 2.2x - 55.

`\hrulefill`

The x-intercept of a line is the point where the line crosses the x-axis. This happens when y is zero.

So, to find the x-intercept of the line y = 2.2x - 55.

We can substitute y=0 into the equation and solve for x.

`\tt 0 = 2.2x - 55`

`\tt 2.2x = 55`

`\tt x=(55)/(2.2)`

`\tt x = 25`

Therefore, the x-intercept of the line is (25,0).

`\hrulefill`

The y-intercept of a line is the point where the line crosses the y-axis.

This happens when x is zero.

So, to find the y-intercept of the line y = 2.2x - 55, we can substitute x=0 into the equation and solve for y.

y = 2.2(0) - 55

y = -55

Therefore, the y-intercept of the line is (0,-55).

The x-intercept and y-intercept of the line are (25,0) and (0,-55), respectively.

Answer 2

`\textsf{$x$-intercept:}\quad \left(\:\boxed{25}\:,\:\boxed{0}\:\right)`

`\textsf{$y$-intercept:}\quad \left(\:\boxed{0}\:,\:\boxed{-55}\:\right)`

Explanation:

x-intercept

The x-intercept of a graphed line is the point at which the line crosses the x-axis, so when y = 0.

From observation of the given graph, the line crosses the x-axis when x = 25. Therefore, the x-intercept is (25, 0).

`\hrulefill`

y-intercept

The y-intercept of a graphed line is the point at which the line crosses the y-axis, so when x = 0.

From observation of the given graph, the line crosses the y-axis when y = -55. Therefore, the y-intercept is (0, -55).